differential equation problem

the graph of a non-negative differentiable function passes through
origin and (1, 2/pi). if, for every x>0, the ordinate set of function
above the interval [0,x] sweeps out a solid of volume x^2f(x) when
rotated about the x-axis, find the function.

( appostol, Calculus vol.1, chapter 8)

i have digged something. how to solve differential equation such as
yy' = x^2y'' + 4xy' + 2y
homogeneous part of equation is easy. but how about non-homogeneous
part. y = f(x) where f is function mentioned above,
.