When n=0, the right side of the equation is-1, and the left and right sides are multiplied by x 2 to get the integral about x.

x^2*y'=-x^3/3+C

Divide both sides by x 2 to get y' =-x/3+c/x 2.

Integral on both sides: y =-x 2/6-c/x+d

Obviously, the equation cannot satisfy the initial conditions, because x=0 requires C=0, while y(0)= 1 gives D=7/6.

This cannot satisfy the condition that y'(0)=0.