# Analytical Integral

GROUPS:
 Hi GuysCan 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
1 year ago
6 Replies
 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.
1 year ago
 Hi SeanYeah you can do a substitution for the U on RHS:y = integral ( o to tau) U(t)dtthen dy/dt = THE WHOLE RHS with y instead of the U integralThe 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 equationMayur
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.
1 year ago
 Hi SeanI tried it (DSolve) and had issues with it, thus I posted here.I would really appreaciate it if you could help me with it.ThanksMayur
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.
1 year ago
 Hi SeanI 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