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Sapphire III

## Toolbox: Solving Ordinary Differential Equations symbolically

As of now it is possible to solve Ordinary Differential Equations (ODE) symbolically in Mathcad, as long as:

-the ODE is linear (does not involve powers or products of the sought function or its derivatives), and

-the coefficients of the derivatives are constant (do not depend on the independent variable).

This means you can solve:

The result is:

Check out the attachments for further information.

The solver "LODEsolve" (reference file for insertion in your sheet) and an example usage file "LM_20200923_LODEsolve" are attached.

If you're using:

- Mathcad 11, use LODEsolve.mcd (it will NOT work in Mathcad 15) and check out example file LM_20200923_LODEsolve.mcd.

- Mathcad 15 use LODEsolve.xmcd  and check out example file LM_20200923_LODEsolve.xmcd.

If you're using (any version of) mathcad Prime: Install Mathcad 15 and use that before you can benefit.

Comments, kudos and suggestions for improvement are welcome.

Success!
Luc

(Thank you @Werner_E for conversion to and checking of Mathcad 15 functionality.)

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1 ACCEPTED SOLUTION

Accepted Solutions

## Re: Toolbox: Solving Ordinary Differential Equations symbolically

Found an error in the symbolic processing of the Mathcad 15 edition of LODEsolve, as a result of which it wouldn't solve sets of ODEs.

That is corrected now.

Luc

7 REPLIES 7
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## Re: Solving Ordinary Differential Equations symbolically

Dear Luc & Werner thank you for these nice worksheets and for the continuous support both of you provide to the Collaboratory. I have learned so much from you both. Best regards, Filip

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## Re: Toolbox: Solving Ordinary Differential Equations symbolically

Update:

It is now also possible to solve sets of Linear Ordinary Differential Equations.

An example:

See attached, and enjoy.

Luc

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## Re: Toolbox: Solving Ordinary Differential Equations symbolically

Congratulations! So you finally succeeded to make it work in MC14/15, too? I had not taken a closer look yet - what was the problem with the earlier attempts?

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## Re: Toolbox: Solving Ordinary Differential Equations symbolically

Things that Mathcad 11 can do, but 15 won't.

Luc

## Re: Toolbox: Solving Ordinary Differential Equations symbolically

Found an error in the symbolic processing of the Mathcad 15 edition of LODEsolve, as a result of which it wouldn't solve sets of ODEs.

That is corrected now.

Luc

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## Re: Toolbox: Solving Ordinary Differential Equations symbolically

Dear Luc, thanks to a friend I can use MC11. However I find something strange when loading your worksheet everything seems to work fine with exception of example 1, 17 and 18 where I get the message "No symbolic result was found". Do you have any idea why this happens? As you did not see the problem I have added a print screen

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Sapphire III
(in response to FDS)

## Re: Toolbox: Solving Ordinary Differential Equations symbolically

Just encountered this:

It also happens when a gets an index subscript. It does NOT happen when y, t or fixed get a subscript. I have no clue (yet) what causes it 😲.

And it does not appear to happen in Mathcad 15...😮

Luc

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