Math 293 Practice Prelim #2Spring 2000(The actual exam will probably be five problems rather than six.)1. Find the solution of the initial value problemd2xdt2+ 2dxdt+ 5x= 0withx(0) = 0 anddxdt(0) = 1.2. Find the solution of the initial value problemtdydt=y+t2sint,withy(π) = 1.3. Find the general solution of the differential equationd2ydt2+ 2dydt+y= 14 cos 3t.4. Find a solution to the equationdydx=y1-x2that satisfies the initial conditiony(0) = 1.5. (a) Show that the vector field
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