Convert the Bessel equation $x^{2}y''+xy'+(\lambda x^{2}-\alpha^{2})y=0$ to integral equation.

Question

Convert the Bessel equation $x^{2}y''+xy'+(\lambda x^{2}-\alpha^{2})y=0$ to integral equation, where $0<x<1,$ $y (x)$ is bounded as $x\to 0$, $y(1)=0$, where $\alpha>0. $ Please give some hint to solve this.