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Toolbox: Solving Ordinary Differential Equations symbolically

LucMeekes
23-Emerald 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:

LucMeekes_0-1600934377296.png

The result is:

LucMeekes_3-1600934433111.png

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.)

1 ACCEPTED SOLUTION

Accepted Solutions
LucMeekes
23-Emerald III
(To:LucMeekes)

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

 

View solution in original post

8 REPLIES 8
FDS
12-Amethyst
12-Amethyst
(To:LucMeekes)

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
23-Emerald III
(To:LucMeekes)

Update:

 

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

An example:

LucMeekes_0-1602697020488.png

See attached, and enjoy.

 

Luc

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
23-Emerald III
(To:Werner_E)

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

See the other thread.

 

Luc

LucMeekes
23-Emerald III
(To:LucMeekes)

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
12-Amethyst
12-Amethyst
(To:LucMeekes)

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

FDS_0-1602761070676.png

Thanks for your help!

LucMeekes
23-Emerald III
(To:FDS)

Just encountered this:

LucMeekes_0-1603057545662.png

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
23-Emerald III
(To: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.

LucMeekes_0-1662734533824.png

Success!
Luc

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