1. Consider the following differential equation with initial conditions:
t^{2} x'' + 5 t x' + 3 x = 0, x(1) = 3, x'(1) = -13.
Assume there is a solution of the form: x (t) = t r
a. Show how to find the possible values of r.
b. Show how to use the initial conditions to find a particular solution.
c. Graph your solution on the interval 0 ≤ t ≤ 10. See if you can use Maple to produce and print your graph.