Finding the Eigenvalue Expansion
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Find the eigenvalue solution of:
y^ IV = 0
y (0) = y' (0) = y (a) = y'(a) = 0
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Solution Summary
Finding the eignevalue expansion of a fourth order initial value problem.
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 ...
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