# LT2

From Example Problems

Create a new moving coordinate system

Translate the derivatives to the new system.

The DE written in the new variables is

Now transform . The new BVP is

Solve this ODE

To have a solution that's bounded at infinity, we must set

Plugging in the BC,

The solution is the inverse Laplace transform of this function. It can be done with convolution.

Everything in the integrand except is called the Green's function for this problem.