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    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

    © BrainMass Inc. brainmass.com October 10, 2019, 5:31 am ad1c9bdddf
    https://brainmass.com/math/linear-algebra/eigenvalue-expansion-508269

    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.

    $2.19