Question 1 (20 pts) Given the initial-value problem By signing this exam you are agreeing that you have neither received nor given assistance on this test. 8 y' + 3xy = 5x ; y(0) = = Separable En (a) Classify the DE by type, order, and linearity. (b) Give an interval / where the solution is defined and unique. (c) Solve the above IVP. Question 2 (30 pts) (a) Find the general solution of the given differential equation. (b) Give the largest interval over which the general solution is defined. Question 3 (20 pts) xy' +(3x+1)y=e-x (a) Show that a one-parameter family of solutions of the equation Liver Grate von (4xy + 3x)dx+(2y+ 2x)dy = 0 is x + 2xy + y = c Muy (do) + Nlay) dy = (b) Show that the initial conditions y(0) = -2 and y(1) = 1 determine the same implicit solution. (c) Find the explicit solutions y(x) and y2(x) of the differential equation in part (a) such that y(0) = -2 and y2(1) = 1. Question 4 (30 pts) Solve the given initial-value problem: y" +4y' + 4y = (3+x)e-2x, y(0) = 2, y'(0) = 5 Cheating will not be tolerated. Cheating includes (but is not limited to) any communication (written or oral) during examinations, using notes during the exam, sharing a book and sharing of work. This includes copying homework assignments from any source. You are required to have reviewed the LTU Academic Honor Code which went into effect in the Fall of 2004. STUDENTS WHO CHEAT ON ANY ASSIGNMENT OR DURING ANY EXAMINATION WILL BE ASSIGNED A FAILING GRADE FOR THE COURSE.