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# test2-1 - Answer characteristic polynomial is with roots so...

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MATH 315 FALL 2006 TEST 2 KEY 1. (20 pts.) Consider the differential equation . 1. Find the general solution for the equation. Answer: characteristic polynomial is , with roots 0, -1, 2. The general solution is therefore 2. Determine the Wronskian for your fundamental solution set. 3. Determine the solution that satisfies initial conditions , , . the solution to the linear system is , , . Final solution:

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2. (16 pts.) Find the general solution for the differential equation . Answer: characteristic polynomial is , with roots , so A particular solution should have the form Final solution: . 3. (15 pts.) Suppose the general solution to a order homogeneous equation is Determine the general form that would be used with the method of undetermined coefficients for the solution to the nonhomogeneous equation