Differential Equation with Coefficients as Integral Functions

I would like to solve a differential equation e.g. in the form: y"+f(x)y'=0 where the coefficient function can only be given as an integral and not explicitly.

Can Matlab solve differential equations of this form?

Answer 1

[Torsten]

fun=@(x,y)[y(2);-y(2)*integral(@(z)z.^2+3*z-1,0,x)];

is a suitable function to be used with ODE45, and it represents your differential equation for

f(x) = integral_{z=0}^{z=x} (z^2+3z-1) dz

Best wishes

Torsten.