Integral equation exercise

Question

Let $\phi \in L^2\left(-\infty,\infty\right)$ and $|x|\geq a$. I have that the following integral equation for $\left(\partial\phi/\partial y\right)\left(z,0,t\right)$: $$\frac{\partial\phi}{\partial y}\bigg\lvert_{y=0}=\frac{1}{\pi}P.V\int_{-a}^a\frac{\left(\partial\phi/\partial y\right)\left(z,0,t\right)}{x-z}dz.$$ I know that the solution is given by: $$\frac{\partial\phi}{\partial y}\left(x,0,t\right)=\frac{C}{\sqrt{a^2-x^2}}+\frac{1}{\pi}P.V\int_{-a}^a\sqrt{\frac{a^2-z^2}{a^2-x^2}}\frac{\left(\partial\phi/\partial x\right)\left(z,0,t\right)}{x-z}dz,$$ where C is an arbitrary constant. Any hint to get that result?