Question 2 (25 points) 2-1. (12 points) Given the following second order ODE x2y" - xy + y = 0 Eq. (Q2-1) (a). (5 points

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Question 2 25 Points 2 1 12 Points Given The Following Second Order Ode X2y Xy Y 0 Eq Q2 1 A 5 Points 1 (38.18 KiB) Viewed 18 times

Question 2 (25 points) 2-1. (12 points) Given the following second order ODE x2y" - 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. 2-2. (13 points) Solve the following initial value problem y" - 2y' + y = 2e* + 2sinx and y(0) = 0, y'(0) = 0. Eq. (Q2-2)