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

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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 = 30cos 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 ² 7. ( D 3 - 2 D
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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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This note was uploaded on 02/02/2011 for the course MATH MAT 2384 taught by Professor Khoury during the Spring '10 term at University of Ottawa.

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