# How to use the Laplace transform of the option PDE to derive ordinary differential equations?

The Black-schole PDE
$$frac{partial V}{partial t}+frac{1}{2}sigma^2S^2frac{partial^2 V}{partial S^2}-rV+rSfrac{partial V}{partial S}=0$$

How to use the Laplace transform and the inversion method to solve it
The bound condition is $$V(0,t)=0$$