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RP_101504734-Participant
4-Participant
May 20, 2024
Solved

symbolic integration with initial condition

  • May 20, 2024
  • 2 replies
  • 1494 views

Hi - how do I tell Mathcad Prime to include an initial condition when symbolically integrating?  I want the initial value of my function to be 0.1 at time t=0. 

 

See attached.

 

thank you,

russ

Best answer by LucMeekes

You have:

LucMeekes_0-1716234417962.png

(I've added an integration constant c)

and want:

LucMeekes_2-1716234490165.png

This means that c will be a function of omega and theta, as follows:

LucMeekes_1-1716234437563.png

With that you can (re-) define:

LucMeekes_3-1716234584629.png

Success!
Luc

 

 

2 replies

W
Werner_E25-Diamond I
25-Diamond I
May 20, 2024

initial? This would mean that you also have to provide an initial value for t. I suppose you mean t=0, that is phi(0)=0.1.

So you actually have a (simple) ODE. Current version of Prime can solve ODEs symbolically:

Werner_E_0-1716233780422.png

Otherwise you could do it step by step:
.) Add an arbitratry constant C of integration
.) Apply the initial condition and solve for C

.) Redefine the function using the correct expression for C

Werner_E_1-1716233900165.png

 

or a little bit shorter, avoiding the explicit definition of C

Werner_E_2-1716234896400.png

 

which can be combined in one small program

Werner_E_3-1716235168847.png

 

P10 worksheet attached

 

 

    L
    LucMeekes23-Emerald IV
    23-Emerald IV
    May 20, 2024

    Translated to Prime 9

    L
    LucMeekes23-Emerald IVAnswer
    23-Emerald IV
    May 20, 2024

    You have:

    LucMeekes_0-1716234417962.png

    (I've added an integration constant c)

    and want:

    LucMeekes_2-1716234490165.png

    This means that c will be a function of omega and theta, as follows:

    LucMeekes_1-1716234437563.png

    With that you can (re-) define:

    LucMeekes_3-1716234584629.png

    Success!
    Luc

     

     

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