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Unformatted text preview: Math 293 Practice Prelim #2 (The actual exam will probably be five problems rather than six.) 1. Find the solution of the initial value problem d2 x dx + 5x = 0 +2 2 dt dt with x(0) = 0 and dx (0) = 1. dt Spring 2000 2. Find the solution of the initial value problem t dy = y + t2 sin t, dt with y() = 1. 3. Find the general solution of the differential equation d2 y dy + y = 14 cos 3t. +2 2 dt dt 4. Find a solution to the equation dy y = dx 1 - x2 that satisfies the initial condition y(0) = 1. 5. (a) Show that the vector field F = (sec2 x + ln y) i + ( x + zey ) j + ey k is conservative. y (b) Calculate the value of the integral
r2 r1 F dr along any path from r1 = 4 i + j to r2 = j + k. 6. Find, by direct calculation, the outward flux of the vector field F = xz i + yz j + k through that part of the sphere x2 + y 2 + z 2 = 25 that is above the plane z = 3. ...
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