Question 2 (25 points) 2-1. (12 points) Given the following second order ODE xºy" - xy' + y = 0 Eq. (Q2-1) (a). (5 point

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Question 2 25 Points 2 1 12 Points Given The Following Second Order Ode Xoy Xy Y 0 Eq Q2 1 A 5 Point 1 (34.56 KiB) Viewed 27 times

Question 2 (25 points) 2-1. (12 points) Given the following second order ODE xºy" - xy' + y = 0 Eq. (Q2-1) (a). (5 points) By inspection, it is known that y = x is a solution of Eq. (Q2-1). Find another solution of Eq. (Q2-1) that is linearly independent with y = x; (b). (2 points) Use the Wronskian of the solution y = x and the other solution you have obtained above to prove that the two solutions are linearly independent; and (c). (5 points) Solve the initial value problem with Eq. (Q2-1) and y(1) = 3 and y'(1) = 2.