Toolbox: Solving Ordinary Differential Equations symbolically

[LucMeekes]

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.)

[FDS]

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

[LucMeekes]

Update:

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

An example:

See attached, and enjoy.

Luc

[Werner_E]

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?

[LucMeekes]

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

See the other thread.

Luc

[LucMeekes · Accepted solution]

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

[FDS]

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

Thanks for your help!

[LucMeekes]

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

[LucMeekes]

Solving the same Linear Ordinary Differential Equations as those supported by my LODEsolve function in Mathcad (15 or 11) is also possible in Prime (7 and up), but not in the same fashion. See attached sheet (Prime 7) for a method.

Success!
Luc