m206_reviewtest2_sp09

m206_reviewtest2_sp09 - Spring 2009 Monika Brannick...

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Unformatted text preview: Spring 2009 Monika Brannick Differential Equations - Math 206 Review Test 2 Note: This is not a sample test. I consider all homework assignments and examples given in class as fair game for the test. 1. Find the general solution of (a) y 00 + y = 3cos2 x (b) y 00 + y = 3cos x 2. Use reduction of order (DO NOT USE THE FORMULA) to find a second, linearly independent solution of xy 00- ( x + 1) y + y = 0 given that y 1 = e x is a solution. 3. Guess the particular solution using the method of undetermined coefficeints. y 000 + 9 y = x 2 e 2 x + x sin x 4. Find a particular solution of x 2 y 00 + xy + y = ln x given that the complementary solution is y c = c 1 cos(ln x ) + c 2 sin(ln x ) . 5. Solve the differential equation y 00- 4 y + 4 y = (12 x 2- 6 x ) e 2 x by variation of parameter subject to the initial conditions y (0) = 1, y (0) = 0. Applications Recall that when different weights are attached to an elastic spring suspended from a fixed support, the spring will stretch by an amount...
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