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Unformatted text preview: y = e-t , with y (0) = 1, y '(0) = 1. Answer: Characteristic polynomial is r 2 +2 r +2, with roots , so . A particular solution should have the form Y ( t ) = Ae-t . 5. (15 pts.) Suppose the general solution to an n th order homogeneous equation L [ y ]=0 is Determine the general form that would be used with the method of undetermined coefficients for the solution to the nonhomogeneous equation Answer: 6. (20 pts.) Use the variation of parameters method to solve the differential equation y ''+3 y '+2 y = 4 e t . Answer: Characteristic polynomial is r 2 +3 r +2 = ( r +1)( r +2), with roots -1, -2; y c ( t ) = c 1 e-t + c 2 e-2 t . Let Y ( t ) = u 1 ( t ) e-t + u 2 ( t ) e-2 t ; then Therefore y ( t ) = y c ( t ) + 2 e 2 t e-t- 4 e 3 t e-2 t /3 = y c ( t ) + 2 e t /3....
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