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SampleExamII-Math305

# SampleExamII-Math305 - geneous diﬀerential equation NHE y...

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MATH 305-002 NAME: October 12, 2009 SAMPLE EXAM II THIS IS A SAMPLE EXAM INTENDED FOR PRACTICE ONLY . THE EXAM MIGHT BE DIFFERENT AND MIGHT INCLUDE MORE QUESTIONS (A) Solve the initial value problem y 00 + 8 y 0 - 9 y = 0 , y (1) = 1 , y 0 (1) = 0 . (B) Find the solution of the initial value problem 16 y 00 +24 y 0 +9 y = 0 , y (0) = 0 , y 0 (0) = 2 .

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2 (C) Verify that the functions y 1 = x and y 2 = sin x form a fundamental set of solutions of the differential equation: (HE) (1 - x cot x ) y 00 - xy 0 + y = 0 , 0 < x < π. (D) Find the solution of the nonhomogeneous differential equation ( NHE ) y 00 + 3 y 0 - 4 y = 10 te t , y (0) = 0 , y 0 (0) = 0 .
3 (E) Use the variation of parameters method to find the general solution of the nonhomo-
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Unformatted text preview: geneous diﬀerential equation ( NHE ) y 00 + 4 y = 3csc t. (F) Give the form of the particular solution in each of the following cases (DO NOT SOLVE for the Coeﬃcients). (i) y 00 + 3 y-4 y = t 2 e t , y p = (ii) y 00 + 3 y-4 y = te-t , y p = (iii) y 00 + 3 y-4 y = e-4 t cos2 t, y p = (iv) y 00 + 3 y-4 y = te-4 t sin t, y p = (v) y 00 + 3 y-4 y = t 2-sin4 t, y p =...
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