Partial Differential Equations : Separation of Variables

Study concepts, example questions & explanations for Partial Differential Equations

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Example Questions

Example Question #1 : Separation Of Variables

Solve for the general solution using separation of variables.

Given the following information:

Possible Answers:

Correct answer:

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.

 

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