Math 293 solution set 8 - try would be y = Ax 2 + Bx + C...

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Math 293 Solutions to Problem Set 8. Here are just the answers to the even-numbered problems. The answers to odd-numbered problems are in the book. More complete solutions will be posted after the problem sets are turned in. § 4.7 #4 . The general solution is c 1 e t + c 2 e 3 t + te t . § 4.8 #2 . A particular solution is y = - 10. #8 . A particular solution is y = sin 2 x . #22 . The homogeneous equation has solutions y = 1 and y = e 7 x . To get a particular solution of the nonhomogeneous equation the obvious thing to
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Unformatted text preview: try would be y = Ax 2 + Bx + C but this doesnt work. The reason is that one of the solutions of the homogeneous equation is y = 1, which also has the form y = Ax 2 + Bx + C . So what you have to do is multiply by x , trying for a particular solution of the form y = Ax 2 + Bx 2 + Cx . This works, and gives y =-1 21 x 3-1 49 x 2-2 343 x , so the general solution is obtained by adding this to c 1 + c 2 e 7 x ....
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