# ODE4 - MAP2302 Final (2 pts) 1. Give the solution to y +...

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MAP2302 Final (2 pts) 1. Give the solution to y 0 + (1 /x ) y = 1 , y (2) = 1. (2 pts) 2. If the equation y 00 + y 0 - 6 y = tan t is to be solved using the Method of Variation of Parameters, write the resulting system of equations used in the technique. (Do not solve the system!) (2 pts) 3. Find a particular solution to y 00 + 2 y 0 + y = te 2 t . (2 pts) 4. Find the solution to the following IVP, expressing the answer in terms of a convolution: y 00 + 2 y 0 + 2 y = g ( t ) , y (0) = 0 , y 0 (0) = 0 .

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(2 pts) 5. Solve: (2 x + y ) dx + ( x + y - 2) dy = 0. (2 pts) 6. Classify (separable, etc.) the following equation: y 0 = 2 x + 3 y 5 x - 2 y . (2 pts) 7. If y 1 and y 2 are solutions to the equation ay 00 + by 0 + cy = 0, then what is the name of the the function y 1 y 0 2 - y 0 1 y 2 ? (2 pts) 8. Determine the inverse transform of F ( s ) = e - 2 s ( s 2 - 5 s +13) s 3 - 6 s 2 +13 s .
(2 pts) 9. Determine the Laplace Transform of f ( t ) = te t u ( t - 2) . (2 pts) 10. Solve: x 2 y 00 - xy 0 + 4 y = 0 , x > 0 . (2 pts) 11. Given y 00 + e x y 0 + y = 0 , y (0) = - 2 , y 0 (0) = 2 , e x = X n =0 x n n ! , ﬁnd the value of the coeﬃcient a 3 in a series expansion about x 0 = 0 for y . (2 pts) 12. Given the equation ( x 2 - 9) 2 y 00 +( x - 3) y 0 +5 y = 0 and using the nomenclature from Section 8.6, categorize the point x 0 = 3 .

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(2 pts) 13. Give the general solution to y 00 + 3 y 0 - y = 0. (2 pts) 14. Given 3 x 2 y 00 + xy = 0, use the Method of Frobenius to ﬁnd a recurrence relation for a series solution about x 0 = 0 for y . (2 pts) 15. If a particular solution to the equation
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## This note was uploaded on 12/15/2011 for the course MAP 2302 taught by Professor Tuncer during the Spring '08 term at University of Florida.

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ODE4 - MAP2302 Final (2 pts) 1. Give the solution to y +...

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