singularity at differential equation with MATLAB

I can't solve this differential equation by ode45 beacause it has sig开发者_JAVA百科ularity.

xy"=3xcos(x)+sin(x) ; x(0)=0 , x'(0)=0

can you help me to write ode45 function?

You can use the sinc(x) function, which is defined as sin(π*x)/(π*x), except at x=0 where its value is 1. So, you can rewrite your ODE as:

y'' = 3*cos(x) + sinc(x/π)

which ode45 shouldn't have any trouble solving.