Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

I'm trying to find an analytical solution to the following integro-differential equation:

[itex]

a f'(x)\int_0^x f(x)dx + b f'(x) + a [f(x)]^2 - a f(x) = 0

[/itex]

with initial condition:

[itex]

f(0)=1

[/itex]

This is a simplified problem for which I know the solution: [itex]f(x)=1[/itex].

I'm trying to find a general method to solve this equation that I can use for more complex problems. The main difficulty is the product of the differential and the integral.

Can anyone point me in the right direction? Integral transforms (e.g. Laplace) seem to be the general way to tackle integro-differential equations but I'm not sure how to apply those here.

Many thanks in advance,

Maarten

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# Analytical solution to integro-differential equation

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