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Higher_Nonhomogeneous - 2-9 D 18 y = e 2 x 8 x 3 y 000 7 x...

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MAT 2384-Practice Problems on Nonhomogeneous higher order ODEs-Methods of Undermined Coefficients and the Variation of Parameters For each of the following ODEs, Find the General Solution. If an initial condition is given, find also the corresponding particular solution. 1. y 000 - 2 y 00 - 4 y 0 + 8 y = e - 3 x + 8 x 2 2. y 000 + 3 y 00 - 5 y 0 - 39 y = 30 cos x 3. y 000 + 3 y 00 - 16 y 0 - 48 y = 112 e 4 x + 60 e x 4. y (4) + 0 . 5 y 00 + 0 . 0625 y = e - x cos(0 . 5 x ) 5. x 3 y 000 + 0 . 75 xy 0 - 0 . 75 y = 9 x 5 . 5 6. ( D 4 + 10 D 2 + 9) y = 13 e 2 x + e - 2 x 2
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Unformatted text preview: 2-9 D + 18) y = e 2 x 8. x 3 y 000 + 7 x 2 y 00 + xy-16 y = 9 x ln( x ) 9. y (4)-26 y 00 + 25 y = 50(1 + x ) 2 , y (0) = 12 . 16 , y (0) =-6 , y 00 (0) = 34 , y 000 (0) =-130 10. y (4)-4 y 000 + 5 y 00-4 y + 4 y = 3cos( x ) + 2 xe 2 x 11. y 000-3 y 00 + 4 y =-2 xe 2 x + 5 3 e 2 x 12. y 000 + 6 y 00 + 11 y + 6 y = 1 1+ e x 1...
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