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WeiXu8-Gravel
8-Gravel
October 4, 2020
Question

Symbolic Differential Equations with Initial Symbolic Value

  • October 4, 2020
  • 2 replies
  • 2267 views

Hi All,

I just figured out how to use prime 6 to solve differential equations both for numerical and symbolic. And if I set the initial value for numerical solving as 0, the results are exactly same with that of symbolic solving. But if I set the initial value for numerical solving not equals 0. The symbolic solving is hard to get the same results. 

I learned how to solve differential equations in this video: https://www.youtube.com/watch?v=7xgvPoL_KMg, from 14:00 to 30:00. The examples in this video are based on initial values equal 0. 

So could anyone let me know is there a way to solve symbolic differential equations with symbolic initial value?

Thanks.

2 replies

W
Werner_E25-Diamond I
25-Diamond I
October 4, 2020

You should attach your sheet with an example so we can see which problem you experience.

 

And ... Prime provides no way to solve a differential equation symbolically in an automatic way! But it may help you solving it manually by using Primes symbolic integration or symbolic Laplace and inverse Laplace transform.

 

W
WeiXu8-GravelAuthor
8-Gravel
October 4, 2020

Hi, 

Please see details in the attachment. I used both numerical and symbolic calculation, and drew the time domain curves. We can find the curves are not same. So could I get the same curve using symbolic solving compared to the numerical one?

Thanks.

W
Werner_E25-Diamond I
25-Diamond I
October 5, 2020

Obviously Luc answered your question even before you posted your file 😉

L
LucMeekes23-Emerald IV
23-Emerald IV
October 4, 2020

This is because Tim forgot to tell you an important detail.

The laplace transform of the derivative of x(t) is not simply s*X, but it is:

LucMeekes_1-1601845522582.png

Likewise, the laplace transform of the second derivative of x isn't simply s^2*X, but:

LucMeekes_2-1601845802704.png

There's your other initial condition.

In Tim's example that doesn't matter, because he had both initial conditions set to 0.

Now, if you name your initial conditions x(0)=x0, and x'(0)=x'0, then the full symbolic solution to the differential equation of the spring system:

LucMeekes_4-1601846205193.png

 

should be:

LucMeekes_3-1601846139985.png

(This expression probably will NOT show, as it is too large to display, it spans several pages).

If you want to take this further, I'll point you to:

- Install Mathcad 15 (as a licensed user of Prime, you can also install and use Mathcad 15 using the very same license file that you used in the installation of Prime)

- check out this item:https://community.ptc.com/t5/PTC-Mathcad/Toolbox-Solving-Ordinary-Differential-Equations-symbolically/m-p/689336#M192090

 

Success!

Luc

 

 

 

 

 

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