Differential equation - maple, Mathematics

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1. Consider the following differential equation with initial conditions:

t² 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.

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