(2) \(\displaystyle x\frac{d^2 z}{dx^2 }+(x+1)\frac{dz}{dx}+(n+1)z=0\).

(3) \(\displaystyle \frac{d^2 y}{dx^2 }+c^2 y =\phi(x) \: , c\in \mathbb{R}\:\) .

(4) If \(\displaystyle xy''+2(\lambda +1 )y' +xy =0 \: , \: \lambda>-1\) , prove \(\displaystyle y(x)=\int_{0}^{1} (1-t^2 )^\lambda \cos(xt)dt\).