All Partial Differential Equations Resources
Example Question #1 : Separation Of Variables
Solve for the general solution using separation of variables.
Given the following information:
Since the question states to use separation of variables the solution looks as follows.
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.