# PDEFT5

From Example Problems

Auxiliary condition: is bounded. |

Since and both range over the whole line, they should both be transformed.

Assume that a solution exists in the form

Take the second partial derivative with respect to z of both sides.

The solution to the ODE is:

To satisfy the auxiliary boundedness condition, we must set .

So the solution is the inverse transform.

Use the boundary condition now.

Finally the solution is