Second_Order_Nonhomogeneous

# Second_Order_Nonhomogeneous - 2 y 00 + xy-1 4 y = 3 x + 3 x...

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MAT 2384-Practice Problems on Nonhomogeneous second 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 00 + 3 y 0 + 2 y = 30 e 2 x 2. y 00 + y = csc( x ) 3. y 00 - 16 y = 19 . 2 e 4 x + 60 e x 4. x 2 y 00 - 2 xy 0 + 2 y = x 3 cos( x ) 5. y 00 + 4 y = 16cos(2 x ) , y (0) = 0 , y 0 (0) = 0 6. y 00 + y 0 - 6 y = 6 x 3 - 3 x 2 + 12 x 7. y 00 - 4 y 0 + 4 y = 12 e 2 x x 4 8. y 00 + y = tan( x ) 9. x 2 y 00 - xy 0 + y = x ln( | x | ) 10. y 00 + 6 y 0 + 73 y = 80 e x cos(4 x ) 11. y 00 - y 0 - 12 y = 144 x 3 + 12 . 5 , y (0) = 5 , y 0 (0) = - 0 . 5 12. y 00 + y = cos( x ) + sec( x ) 13. x
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Unformatted text preview: 2 y 00 + xy-1 4 y = 3 x + 3 x 14. y 00-. 16 y = 32cosh(0 . 4 x ) 15. y 00-2 y + y = x 2 + x-2 e x 16. y 00 + 1 . 44 y = 24cos(1 . 2 x ) 17. y 00 + 9 y = 18 x + 36 sin(3 x ) 18. y 00 + 4 y + 5 y = 25 x 2 + 13 sin(2 x ) 19. x 2 y 00-2 xy + 2 y = x 3 sin( x ) 20. y 00 + 2 y + y = 2 x sin( x ) 21. y 00 + 2 y + 10 y = 17sin( x )-37 sin(3 x ) , y (0) = 6 . 6 , y (0) =-2 . 2 1...
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## This note was uploaded on 02/24/2010 for the course SITE MAT2384 taught by Professor Josephkhoury during the Fall '09 term at University of Ottawa.

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