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Unformatted text preview: y + 9 y = 4 te 3 t + 6 t 2 sin(5 t ) 4. (10 points) Determine the longest interval in which you are sure that a solution of the following intial value problem exists. ( x 29)( x + 1) y 00 + 3 xy4 y = 0 , y (0) = 27 , y (0) = 2 5. (15 points) Given that x and x 4 form a fundamental set of solutions of the associated homogeneous diﬀerential equation, ﬁnd the general solution of y 004 x y + 4 x 2 y = 3 x 2 + 9 x 4 . 6. (15 points) Find the general solution of x 2 y 009 xy + 25 y = 0 on x > 0. 7. (15 points) Find a polynomial solution of the following diﬀerential equation. (1x 2 ) y 002 xy + 20 y = 0...
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 Fall '10
 GODDARD
 Differential Equations, Equations, general solution, Dr. Schurle

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