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LucMeekes23-Emerald IV
23-Emerald IV
September 24, 2020
Solved

Toolbox: Solving Ordinary Differential Equations symbolically

  • September 24, 2020
  • 3 replies
  • 6390 views

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.)

    Best answer by 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

     

    3 replies

    F
    FDS13-Aquamarine
    13-Aquamarine
    September 24, 2020

    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

    L
    LucMeekes23-Emerald IVAuthor
    23-Emerald IV
    October 14, 2020

    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

      W
      Werner_E25-Diamond I
      25-Diamond I
      October 14, 2020

      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?

      L
      LucMeekes23-Emerald IVAuthor
      23-Emerald IV
      October 14, 2020

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

      See the other thread.

       

      Luc

      L
      LucMeekes23-Emerald IVAuthor
      23-Emerald IV
      September 9, 2022

      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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