Homework2_ODE - Find y 2 ; using reduction of order....

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Homework 2 (40 points) Due date: October 16th, 2009 I will only grade 4 problems at random. 1 . pg. 185, ex. 29. 2 y 00 + y = t (1 + sin t ) : 3 . pg. 190, ex. 17. Do not solve using the formula, instead set up the method and show details of your work. 4 to the di/erential equation ty 00 ± (1 + t ) y 0 + y = t 2 e 2 t ; t > 0 ; given that y 1 ( t ) = 1+ t is a solution of the corresponding homogeneous equation. Hint:
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Unformatted text preview: Find y 2 ; using reduction of order. & 5 . pg 214, ex. 6. Set up the initial value problem. Do not solve . & 6 . On the Laplace transforms: pg. 322, ex. 16, 17. & 7 . (a) pg. 330, ex. 8. (b) For the function f ( t ) given above in (a), &nd the solution to the di/erential equation y 00 + y = f ( t ) ; subject to the initial conditions y (0) = 0 and y (0) = 0 : 1...
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