Question: 7. (16 points) Consider the following initial value problem: thy - 3ty' + 4y =0, y(1) = 1, y'(1) = 0 (a) Show that y1

7. (16 points) Consider the following initial value problem: thy" - 3ty' + 4y =0, y(1) = 1, y'(1) = 0 (a) Show that y1 (t) = t2 and y2 (t) = t2 Int are 2 solutions to the ODE thy" - 3ty' + 4y = 0. (b) Show that y1 (t) = t2 and y2 (t) = t2 In t are linearly independent. (c) Find the solution to the initial value

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