Unformatted text preview: e 2 t + c 2 e − t + 1 4 e 3 t . 5. This equation has associated homogeneous equation y − 2 y + y = 0. Its auxiliary equation, r 2 − 2 r +1 = 0, has a double root r = 1. Thus a general solution to the homogeneous equation is y h ( t ) = c 1 e t + c 2 te t . For the variation of parameters method, we let y p ( t ) = v 1 ( t ) y 1 ( t ) + v 2 ( t ) y 2 ( t ) , where y 1 ( t ) = e t and y 2 ( t ) = te t . 214...
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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations, Trigraph, homogeneous equation

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