hi, im havin some problems solving this integral,

if $\displaystyle y= \int_0^\frac{1}{2\pi} \cos(x \sin \theta) d\theta $

show that $\displaystyle xy'' + y' +xy =0$

ive found the integral to be $\displaystyle \frac{\sin(x \sin \theta)} {-x \cos\theta}$ is this correct, i found it using the substitution method where $\displaystyle u = x \sin\theta$

if this integral is correct, how do i solve the rest of the equation?