Consider the following differential equation 32x 2y '' + 3 (1 − e 2x )y = 0 (b) Determine the indicial equation and find its roots. (c) Without solving the problem, formally write the two linearly independent solutions near x = 0. (d) What can you say about the radius of convergence of the power series in (c)? (e) Find the first three non-zero terms of the two linearly independent solutions.
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