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Calculations are the heart of engineering information yet too many companies fail to properly solve, document, and share their engineering calculations. They lose invaluable intellectual property with every new project, resignation or retirement. Mathcad is the first and only engineering calculation solution that simultaneously performs and documents engineering calculations while dramatically reducing the risk of costly errors.

Tutorial - Solving an Ordinary Differential Equation Using Mathcad

This tutorial shows how to solve an Ordinary Differential equation using Mathcad.


Mathcad Express is a free version of Mathcad that allows you to utilise some selected features of Mathcad Prime 3.0, for an unlimited time. Mathcad Express gives you the ability to spend more time solving engineering problems, and less time programming, documenting, reporting and verifying their solutions. Mathcad Express was designed to be a powerful analysis tool – it is easy to learn and easy to use.
Mathcad Express includes the full capabilities of Mathcad Prime 3.0 for 30 days, for free. After the 30 day period has ended, you may continue to use the limited functionality of Mathcad Express as long as you like - the Mathcad Express license will never expire. You can expect to see in-product messages with information on selected features, training, tips and tricks, and easy ways to purchase the full commercial product. You will also see specific “Mathcad Express” headers and watermarks on worksheets. Should you decide to upgrade to the full product, you will receive the full breadth of Mathcad capabilities and you can eliminate in-product advertising and watermarks.


If you have purchased a license, this demo will convert to a fully licensed version upon entering your authorisation code into the program.

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1.1         Hearne provides software solutions to its Customers based on IBM SPSS Software and is authorised to provide IBM SPSS Software on the terms and conditions set out in this Licence.

1.2         This Licence together with Hearne’s Invoice and/or Online Order confirmation, constitute a contract that applies between Hearne and the Licensee from the Commencement Date in respect of any use by the Licensee of Hearne's software solutions and support incorporating IBM SPSS Software supplied by Hearne to the Licensee.

1.3         The Licensee acknowledges that it is not a licensee of IBM and all of the Licensee's rights and remedies relating to the provision of IBM SPSS Software are with Hearne and are as set out in this Licence.


2.1         In consideration of the entry into this Licence and payment of Hearne’s Invoice and/or Online Order by the Licensee, Hearne agrees to provide to the Licensee a non-exclusive licence to use the IBM SPSS Software for the term specified in Hearne’s Invoice and/or Online Order.

2.2         This Licence grants to the Licensee the rights to:

(a)          Utilise the IBM SPSS Software specified in Hearne’s Invoice and/or Online Order for the number of Users or any Authorised Uses and/or as specified in IBM's licence material;

(b)         When eligible, be provided with upgrades to the IBM SPSS Software as well as any support from Hearne as set out in Hearne’s Invoice and/or Online Order confirmation; and

(c)          Otherwise utilise the IBM SPSS Software licensed by Hearne in accordance with this Licence.

2.3         Unless the Licensee purchased a fixed term licence or otherwise notified in writing by Hearne under these Terms, this Licence is a perpetual licence commencing from the date of Hearne’s Invoice and/or Online Order.


3.1         Hearne warrants that the IBM SPSS Software, when operated in accordance with accompanying documentation and in its specified operating environment, will conform to its specifications. If within the first 30 days of the date of Hearne’s Invoice and/or Online Order confirmation the SPSS Software does not function to its specifications the Licensee may return it to Hearne and receive a refund of the amount the Licensee paid after which this Licence terminates.

3.2         Hearne warrants that it has the rights from IBM to licence the SPSS Software as set out in this Licence and is fully able to licence such rights to the Licensee in accordance with this Licence.

3.3         Hearne shall provide the Licensee with updates and information in respect of or related to the IBM SPSS Software that Hearne deems may assist the Licensee in fully utilising or supporting the benefit of the licence provided to the Licensee under this Licence.

3.4        Hearne shall promptly supply the Licensee with the IBM SPSS Software ordered by the Licensee by making such software available for download by the Licensee from Hearne or, for an additional cost, on usual electronic medium (such as DVD) and such expertise, technical information and know-how as Hearne may reasonably determine is required by the Licensee in order to obtain the benefits of the rights granted to it under this Licence


4.1        The Licensee shall ensure that the IBM SPSS Software is only used in accordance with these terms, Hearne’s Invoice and/or Online Order confirmation and take all reasonable steps to ensure that all IBM SPSS Software is secure from copying or any other tampering or use by any third party that is not permitted by law or under the terms of this Licence.

4.2        The Licensee shall:

(a)          Operate and otherwise utilise the IBM SPSS Software in accordance with IBM's specifications and informational material;

(b)         Advise Hearne promptly by notice in writing of any act or omission of any party coming to the attention of the Licensee that may or shall breach the terms of this Licence.

4.3         The Licensee shall not integrate the IBM SPSS Software with any other software (either object or source code) except as permitted by the terms of this Licence.

4.4        The Licensee acknowledges that other than those rights which are contained in this Licence, Hearne has not conferred upon the Licensee any proprietary rights to an interest in any Intellectual Property.

4.5        The Licensee acknowledges and agrees that it is responsible to ensure that it or any of its Users comply with any and all relevant requirements of this Licence and is fully liable to Hearne for any act or omission of it or it’s Users which are in breach of this Licence.


5.1         The Licensee acknowledges that it is responsible for its own computer hardware and software and properly integrating the IBM SPSS Software with the Licensee's own computer system and Hearne is not responsible for any failure or errors in the IBM SPSS Software that are caused by the IBM SPSS Software being utilised on or with incompatible hardware and software and provides no warranty in respect of such compatibility.

5.2         Hearne is not bound or liable for any error or omission in or generated by the IBM SPSS Software.

5.3         Hearne shall not be responsible for any Damages caused by third party virus, Trojan horse, software bomb, malware or any other similar third party act.

5.4         Except as otherwise warranted by Hearne in writing, the Licensee acknowledges that it must rely upon its own judgment as to the nature, quality and condition of the IBM SPSS Software supplied by Hearne and as to its sufficiency for any use or purpose and the Licensee acknowledges that Hearne is under no duty to ascertain the suitability of the IBM SPSS Software licensed by it in respect of any purpose whatsoever and that no such representation has been made by Hearne.

5.5         Except for any express written warranty in this Licence or otherwise provided to the Licensee, Hearne provides no other warranty, express or implied, including any implied warranty of merchantability or fitness for purpose or otherwise and any warranties expressed or implied by law or statute, in respect of goods whether in respect of quality, fitness for intended purposes or otherwise, are excluded to the extent that such law or statutes permit exclusion.

5.6         The Licensee acknowledges and agrees that IBM is entitled to withdraw programs (and related licensing rights to those programs) based on infringement claims in respect of those programs or a loss of rights by IBM in the programs. Should IBM withdraw programs and licences then Hearne and the Licensee shall immediately cease to use such programs. In the case of licenses limited by time, the Licensee’s sole remedy for such a withdrawal of licensing rights is a pro rata refund in respect of the unexpired portion of the term granted by Hearne in the related software.

5.7         Hearne will not be liable for:

(a)          Any loss by any third party not being a party to this Licence;

(b)         Any special, incidental, indirect, punitive or consequential Damages; loss of profit, revenue, goodwill, use or the costs of procuring substitute goods or services;

(c)          Damages, in the aggregate, exceeding the value of Fees actually received by Hearne from the Licensee under this Licence; or

(d)         Any claim or action that shall be brought more than six months after the Licensee became aware, or reasonably ought to be aware of the circumstances giving rise to the action.


6.1         Hearne owns or fully licenses all of the Intellectual Property from third parties and in the case of the IBM SPSS Software licenses such software from IBM and in respect of all Intellectual Property provided by Hearne the Licensee acknowledges and agrees that:

(a)          The Intellectual Property is wholly owned by Hearne or fully licensed to it and the Licensee will not contest or challenge title, rights or ownership of any of Hearne's Intellectual Property;

(b)         The Licensee shall only utilise the Intellectual Property licensed to it in accordance with the grant made to it and set out in this Licence or as otherwise agreed with Hearne in writing; and

(c)          Shall observe all rules and regulations for the time being in force in relation to the Intellectual Property (in particular, it shall ensure its Users are otherwise aware that the IBM SPSS Software is owned by IBM and licensed by Hearne) and will carry out all reasonable directions from time to time given to it by Hearne in respect of the IBM SPSS Software.

6.2        In the event of any claim of infringement resulting from or the challenge to the Licensee's use of any of the Intellectual Property the Licensee agrees to immediately notify Hearne of the facts concerning such claim or challenge. Hearne indemnifies the Licensee against any claim made by a third party against the Licensee (including the Licensee's costs and expenses) resulting from the Licensee's proper and lawful use of the Intellectual Property Rights pursuant to the terms of this Licence. The Licensee agrees that Hearne has sole discretion as to what action to take, if any, regarding the claim of such third party. Should Hearne elect to take legal or administrative action in connection with any such matter, the Licensee shall, if required by Hearne, join as a party to such action or to allow the action to be brought solely in the name of Hearne. Hearne further indemnifies the Licensee in relation to the Licensee's reasonable costs and expenses as a result of the Licensee assisting Hearne or being joined as a party to such action.


7.1         Nothing expressed or implied in this Licence shall constitute either party as the partner, agent, employee or officer of, or as a joint venture party with the other party, and neither party shall make any contrary representation to any third person.

7.2         The Licensee shall conduct its business as an independent proprietor and not as partner or agent of Hearne and shall not register any business, trade or other name or style which is the Intellectual Property of Hearne other than on the terms contained in this Licence or otherwise hold itself out as being in any relationship with Hearne otherwise than as its Licensee.


8.1         Neither party shall be liable to the other for any breach or failure to perform any of its obligations under this Licence where such breach or failure is occasioned by a cause or causes beyond the reasonable control of that party including (but without limiting the generality of the foregoing) civil commotion, hostilities, strikes or lock outs and if either party is or is likely to be affected by any such event it shall immediately notify the other party of the occurrence or likely occurrence of the anticipated events and shall use all reasonable endeavours to overcome or mitigate the effects of the force majeure event.


9.1         Any notice given hereunder shall be deemed to have been sufficiently served if physically delivered or communicated by facsimile or e-mail addressed to the last known address of the addressee. If a notice is sent by way of facsimile or e-mail it shall be deemed to have been served when in the ordinary course of transmission it would have been received.


10.1      The Licensee indemnifies Hearne from and against all Damages including those associated with any third party claim, and whether arising under contract, tort (including negligence) or otherwise should Hearne or any of its Personnel sustain or incur (directly or indirectly) that arises out of or results from:

(a)          Any breach of this Licence by the Licensee;

(b)         Any claim by any third party arising from any act or omission of the Licensee in connection with this Licence (whether negligent or not), including in connection with or arising out of the Licensee’s breach of clause 7; or

(c)          Any negligent, wilful, reckless or unlawful act or omission of, or any intentional misconduct by, the Licensee in connection with this Licence; or

(d)         Any claim by the Licensee, to the extent that such claim is beyond the scope of Hearne's liability to the Licensee under this Licence.


11.1      Either party may give the other party notice of any dispute arising in respect of, or in connection with, this Licence ("Dispute").

11.2      In the event of a notice being given pursuant to clause 9.1 above, then the parties must:

(a)          Meet to discuss the Dispute and make a genuine effort to resolve the Dispute;

(b)         If no resolution of the Dispute has occurred within ten (10) Business Days from the date of the giving of the notice in accordance with clause 9.1 above, then either party may pursue their remedies as they see fit.

11.3      Nothing in this clause shall prevent a party making application to a court for an injunction or other urgent interlocutory relief.


12.1      Hearne may suspend or cancel this Licence and cease to provide access to the IBM SPSS Software or any ancillary services:

(a)          If the Licensee:

(i)       Fails to make any payment to Hearne payable in accordance with this Licence or under any other agreement between Hearne and the Licensee within 20 Business Days of such payment falling due;

(ii)       Fails to meet reasonable requirements in respect of or relating to the use or more general business utilisation of the IBM SPSS Software which is advised to the Licensee by Hearne in writing, including any restrictions on use; or

(iii)      Otherwise fails to comply with this Licence or any other agreement with Hearne; and

A suspension of access to the IBM SPSS Software under this clause 12.1 or any refusal or delay by Hearne to provide any related support or service does not constitute a termination of any agreement Hearne has with the Licensee (unless Hearne so advises the Licensee in writing) or breach of any such agreement or these Terms by Hearne.

12.2      Hearne may terminate this Licence if the Licensee is in serious breach of this Licence and has not remedied such breach within 10 Business Days of being given notice to do so by Hearne.

12.3      Either party may terminate this Licence immediately without notice if the other party:

(a)          Enters into liquidation whether compulsorily or voluntarily (other than for the purposes of amalgamation or reconstruction);

(b)         Has a receiver, administrator, or administrative receiver appointed over it or any of its assets or property;

(c)          Becomes subject to statutory management or any similar regime; or

(d)         Compounds with its creditors or takes or suffers any similar action or proceeding in consequence of debt.

12.4      Effect of Termination

Where this Licence has been terminated:

(a)          With immediate effect the licence granted to the Licensee under clause 2 is terminated and the Licensee must immediately uninstall all copies of the IBM SPSS Software licensed under these Terms from its systems and return all "hard copies" of such software to Hearne;

(b)         Within fifteen Business Days from the date of termination, the Licensee must:

(i)      Return or destroy, (at Hearne's option), all copies of Hearne's Intellectual Property, Improvements and Confidential Information (if any) in its possession or under its control, including all such things in the hands of the Licensee's Personnel; and

(ii)      Provide Hearne's Personnel such reasonable access to the Licensee's systems and system information as is necessary to enable Hearne to confirm all such IBM SPSS Software has been uninstalled and deleted and all copies have been returned or destroyed.

13.    GENERAL

13.1      To be effective, any waiver of any or all of the terms and conditions in any agreement a party has with the other party must be in writing.

13.2      A party may not assign all or any of its rights or obligations under this Licence without the prior written consent of the other party.

13.3      Where a party has rights and remedies at law or otherwise in addition to the rights set out in this Licence, those rights and remedies will continue to apply.

13.4      Failure by a party to enforce any of the terms and conditions of this Licence shall not be deemed to be a waiver of any of the rights or obligations that party has under this Licence.

13.5      If any of these terms in this Licence are held to be invalid, illegal, unenforceable or void for any reason or reasons, all of the remaining terms or parts of the Licence (or part thereof) shall remain in full force and effect.

13.6      For Australian customers this Licence is governed by the laws of Victoria, Australia and each party irrevocably and unconditionally submits to the non-exclusive jurisdiction of the courts of Victoria.

13.7      For New Zealand and Pacific Island customers this Licence is governed by the laws of New Zealand and each party irrevocably and unconditionally submits to the non-exclusive jurisdiction of the courts of New Zealand.


14.1      In interpreting this Licence:

"Authorised Use" means the use which the Licensee is authorised to make use of the IBM SPSS Software which may be measured by number of users, millions of service units, processor value units or any other level of use permitted as specified by IBM in respect of the relevant IBM SPSS Software;

"Business Day" means a day not being a Saturday, Sunday or statutory holiday in Melbourne, Victoria, Australia and does not include the period from 20 December to 16 January in any calendar year;

"Commencement Date" means the date of Hearne’s Invoice and/or Online Order Confirmation to the Licensee which provides any IBM SPSS Software in accordance with that invoice, online order confirmation and this Licence;

"Damages" means all liabilities, expenses, losses, damages and costs (including a party's own legal costs on a full indemnity basis) whether incurred by or awarded against a party including those associated with any third party claim, and whether arising under contract, tort (including negligence) or otherwise;

"Fees" means the licence fee and any other fee that may be payable by the Licensee to Hearne in accordance with this Licence or Hearne’s Invoice and/or Online Order;

"IBM" means International Business Machines Corporation or any of its subsidiaries as is relevant to this Licence or the software provided under this Licence;

"IBM SPSS Software" means the IBM SPSS owned, named and branded (with the letters "SPSS") software licensed to Hearne for the purposes of providing licences and related advice and support to Hearne's licensees and customers in Australia, New Zealand and the Pacific Islands and which Hearne provides on the terms set out in this Licence;

“Hearne’s Invoice and/or Online Order” means the relevant invoice and/or online order confirmation sent to the Licensee by Hearne that pertains to the Licensees purchase of IBM SPSS Software and any Improvements;

"Improvements" means any improvement on, modification or alteration of, or enhancement to any part or all of the IBM SPSS Software or any matter relating to the IBM SPSS Software whether directly (updates) or indirectly (add-ons and additional software);

"Intellectual Property" means (whether in visible, electronic or any other form) all intellectual property which Hearne owns or in which Hearne has rights and includes the Brands, IBM SPSS Software and all related trade names, brands, contracts, concepts, goodwill, logos, formulae, techniques, know-how, specifications, designs, drawings, copyright, patents and trademarks (if any) whether registered or not, data, software (in source and object code), business strategies, Improvements and all of Hearne's confidential information;

"Personnel" means employees, agents, contractors, shareholders, principals, officers or directors of a party;

“Term” means the term as specified in Hearne’s Invoice and/or Online Order confirmation;

"User" means the Licensee or a person the Licensee allows to use the Licensee's IBM SPSS Software and that is permitted to do so by the terms of this Licence and the relevant IBM SPSS Software and "Users" means more than one User;

14.2      Interpretation

In the interpretation of these Terms, unless the context otherwise requires:

(a)          References to the parties or a party means the parties or a party to these Terms and includes their respective executors, administrators, successors and permitted assigns;

(b)         References to persons include individuals, partnerships, firms, associations, corporations and unincorporated bodies of persons, government or semi-government or local body or municipal bodies, and agencies or political subdivisions of them in any case whether having separate legal personality or not;

(c)          Words in the singular shall include the plural and vice versa. Words importing one gender shall include the other genders and to this extent "it" shall include "he" or "she" as applicable;

(d)         Any obligation not to do anything includes an obligation not to suffer, permit or cause that thing to be done;

(e)         References to clauses shall be construed as references to the same in these Terms;

(f)          References to "written" or "writing" extends wherever possible to all forms and modes of writing including all forms of medium (including electronic medium) and, without limitation, extends to all information available or provided via website, website links or email;

(g)          Reference to "month" or "months" means a calendar month unless otherwise expressly stated;

(h)         Any covenant that binds any two or more persons or parties shall bind them jointly and each of them severally.


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