Consider the following differential equation:
t^{2} x''+ 5 t x' + (3 + 2 t) x = 0
a. Show the steps needed to derive the recursive formula for the coefficients of the power series.
b. Find all the terms of the power series through degree 5. If there are unknown constants, include them as appropriate.
c. Use Maple to graph the solution for 0 ≤ t ≤ 10. How many terms did you need to include to get good convergence?