# Finding the Eigenvalue Expansion

Find the eigenvalue solution of:

y^ IV = 0

y (0) = y' (0) = y (a) = y'(a) = 0

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#### Solution Preview

The essential steps are:

1. To find the characteristic polynomial to get the eigenvalues.

2. Write a solution that has a term for each eigenvalue.

3. Use the boundary conditions to determine the constants in your solution.

Problem:

Find the eigenvalue solution of :

y^IV=0

y(0)= y^' (0)=y(a)= y^' (a)=0

Detailed Solution:

For any linear, homogeneous DE with constant coefficients, we can use the characteristic polynomial to find the solution. That is replace each derivative of y with an equivalent power of ? i.e. replace ...

#### Solution Summary

Finding the eignevalue expansion of a fourth order initial value problem.

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