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