I'm looking at an integro-differential equation prompted by a HW question. This is a simplified version of it:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{df}{dx}=-\frac{af}{x^2}\left(\int_{x_0}^x u^2f(u)du+M\right);\quad f(x_0)=1[/tex]

with:

[tex]x_0>0[/tex]

and a and M positive constants.

Does anyone know if it can be approached analytically and how? I'm currently working on a modified Runge-Kutta method to solve it numerically . Is that the best approach for such equations?

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# An interesting IDE

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