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7.22, §5 Solve

Expand all variables in the problem for v in a Fourier series:

Put into P.D.E. :

Because of the choice of the X_n:

Put into I.C. :

Solve this O.D.E. and initial condition for C_n:

Homogeneous equation:

Inhomogeneous equation:

Initial condition: .

Next: 7.22, §6 Total Up: 7.22 Previous: 7.22, §4 Eigenfunctions