# secnho_ex - x 24 x = t e 2 t 7 d 2 x dt 2 8 dx xt 25 x =...

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EXAMPLES OF NON-HOMOGENEOUS SECOND ORDER LINEAR EQUATIONS 1 . d 2 y dx 2 - dy dx - 2 y = x 2 . d 2 y dx 2 - dy dx - 2 y = 3 x 2

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3 . y 00 - 16 y = sin (2 x ) , with the initial conditions ± y (1) = 1 y 0 (1) = 0 , given that the general solution of the homogeneous problem is y h ( x ) = c 1 e - 4 x + c 2 e 4 x .
4 . y 00 + 16 y = sin (8 x ) , with the initial conditions ± y (1) = 1 y 0 (1) = 0 5 . z 00 - 2 z 0 + z = e - x , with z (0) = 0 , z 0 (0) = 1 , given that the general solution to the homogeneous problem is z h ( x ) = c 1 e x + c 2 xe x .

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6 . ¨ x + 10 ˙
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Unformatted text preview: x + 24 x = t + e 2 t . 7 . d 2 x dt 2 + 8 dx xt + 25 x = cos (2 t ) , with x (0) = 0 , ± dx dt ² (0) = 1 2 . given that the general solution of the homogeneous equation is x h ( t ) = e-4 t [ c 1 cos (3 t ) + c 2 sin (3 t )]. What result do you get when you replace the right hand side with cos (3 t )?...
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secnho_ex - x 24 x = t e 2 t 7 d 2 x dt 2 8 dx xt 25 x =...

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