# Partial Differential Equations : Separation of Variables

## Example Questions

### Example Question #2 : Second Order Linear Pd Es

Solve for the general solution using separation of variables.

Given the following information:

Explanation:

Since the question states to use separation of variables the solution looks as follows.

Let

therefore the partial differential equation becomes

is some constant therefore making the ordinary differential equation,

In this particular case the constant must be negative.

Solving for  and  results in the following.

From here solve for the general transient solution

Lastly apply the boundary conditions to solve for the constants and in turn solve the general solution.