Can I solve this integral equation ?

here B,C are constants.

initial condition :- f(0,x)= (N0/x0) exp(-x/x0)

N0 and x0 are constants

[darova]

What do you need to find?

[Walter Roberson]

Does N0 = 2/B ?

[Anomitra Saha]

I need to find the function f(t,x).

[Anomitra Saha]

I don't think N0 and B are related. They are separate constants.

[Walter Roberson]

In your equation, substitute t = 0. Then int(f(0,x),x,0,inf) = 2/(B+0*C) = 2/B . This is a given.

We are also given the initial condition that f(0,x) = (N0/x0)*exp(-x/x0) . Integrate that over x = 0 to inf assuming x0>0 to get N0 + C for some constant C. Therefore 2/B = N0 + C . Therefore N0 and B are related.

[Anomitra Saha]

Okay.. but how does that help in finding the solution of my equation?

I need to find f(t,x) in terms of x, t, N0, B, x0.

[Bjorn Gustavsson]

Well what do you get if you write your left-hand side as: ? Can you proceed from there?

[Anomitra Saha]

Can you please elaborate ?

[Bjorn Gustavsson]

Yes (but this is your task to solve for some sort of 1st-2nd year studies, right?). Walter showed you how to determine some parameters in your equation, so you have a good grasp of f(0,x), If you assume that f(t,x) can be written as a product between 2 functions: f(0,x) that only depends on x and one function g(t), how can you proceed from that assumption? Analytical manimpulation of the integral can possibly get you a step forward, don't you think?

[Anomitra Saha]

okay..I got it. Thanks mate.