Question: For the differential equation + 2 3 2 = 0, where is a constant: a) Solve by the method of solution by series and find

For the differential equation + 2 3 2 = 0, where is a constant:

a) Solve by the method of solution by series and find the recursion relation for the coefficients.

b) Assuming the series must cut off after a finite number of terms, find an expression for the allowed eigenvalues of and give the seven smallest values.

c) Find the eigenfunction solutions corresponding to these seven eigenvalues. For simplicity, you may assume that the first non-zero coefficient in each solution is equal to 1.

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