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Analytical Integral

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Hi Guys

Can someone help me to find the analytical solution for the equation below?
I tried it using Mathematica but I am having issues with doing it.

Your help will be greatly appreciated.

Thanks


 
POSTED BY: Mayur Ostwal
Answer
1 year ago
Hi. What is the code you have tried so far? 

I notice that the U(tau) occurs on both the left and right hand side of this equation. So this looks like an integral equation.  

Can you convert this integral equation into a differential equation by some means? Mathematica does not directly solve integral equations.
POSTED BY: Sean Clarke
Answer
1 year ago
Hi Sean

Yeah you can do a substitution for the U on RHS:

y = integral ( o to tau) U(t)dt

then dy/dt = THE WHOLE RHS with y instead of the U integral

The paper I got this equation from said it has a analytical solution if we find it using Mathematica or Maple.

I solved the equation numerically using the above substitution but I need to add something to it and it becomes harder to do it numerically after my modification to the equation

Mayur
POSTED BY: Mayur Ostwal
Answer
1 year ago
Okay. So it looks like you have a way to convert this integral equation into a differential equation. This is good because this can be entered into DSolve, which may be able to find a symbolic solution. 

Have you tried writing out this differential equation in Mathematica's syntax? If not, please take a look at the documentation for DSolve. If you have any questions about how to enter some part of the equation using Mathematica's syntax, please let us know.
POSTED BY: Sean Clarke
Answer
1 year ago
Hi Sean

I tried it (DSolve) and had issues with it, thus I posted here.
I would really appreaciate it if you could help me with it.

Thanks
Mayur
POSTED BY: Mayur Ostwal
Answer
1 year ago
Please if possible, post what code you have for your DSolve statement. This will help me interpret your problem as quickly as possible.

Otherwise, I will take a look at this when I can. 
POSTED BY: Sean Clarke
Answer
1 year ago
Hi Sean

I will try to post it soon. I have not saved my code since i was just trying to learn Mathematica and solve it.
I will try again and post it.

If before then if you find time to do it, I would really appreciate it.

Mayur
POSTED BY: Mayur Ostwal
Answer
1 year ago