Math 293 practice prelim 2

Math 293 practice prelim 2 - Math 293 Practice Prelim#2(The...

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Math 293 Practice Prelim #2 Spring 2000 (The actual exam will probably be five problems rather than six.) 1 . Find the solution of the initial value problem d 2 x dt 2 + 2 dx dt + 5 x = 0 with x (0) = 0 and dx dt (0) = 1. 2 . Find the solution of the initial value problem t dy dt = y + t 2 sin t, with y ( π ) = 1 . 3 . Find the general solution of the differential equation d 2 y dt 2 + 2 dy dt + y = 14 cos 3 t. 4 . Find a solution to the equation dy dx = y 1 - x 2 that satisfies the initial condition y (0) = 1. 5 . (a) Show that the vector field
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