6_HW - If initial conditions are given, find the solution...

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Math 2233 Homework Set 6 1. Solve the following Euler-type equations. (a) x 2 y + xy = y =0 (b) x 2 y - xy +2 y =0 (c) 4 x 2 y - 4 xy +3 y =0, y (1) = 0, y (1) = 1 (d) x 2 y - 3 xy +3 y =0 (e) x 2 y +5 xy +5 y =0 2. Given that y 1 ( x )= e x and y 2 ( x )= x are solutions of (1 - x ) y + xy - y =0 find the general solution to (1 - x ) y + xy - y =2( x - 1) 2 e - x by the method of Variation of Parameters. 3. Find the general solution of each of the following equations by the method of Variation of Parameters.
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Unformatted text preview: If initial conditions are given, find the solution satisfying that initial value problem. (a) y-3 y + 2 y = 10 (b) y + y = sin( x ), y (0) = 1, y (0) = 2 (c) y-7 y + 10 y = 100 x (c) y + 4 y = sec(2 x ) 4. Use the method of Variation of Parameters to solve the following non-homogeneous Euler-type equation. x 2 y-5 xy + 9 y = x 3 1...
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This homework help was uploaded on 04/22/2008 for the course MATH 2233 taught by Professor Binegar during the Spring '08 term at Oklahoma State.

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