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WrittenAssign1 - 6 Solve the initial value problem y 00 4 y...

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MATH 263, WRITTEN ASSIGNMENT 1 Due Thursday, February 7th 2008, by noon, at the Math Dept Office (BH1005). 1. Solve the initial value problem xy 0 + 2 y = x 2 - x + 1 , y (1) = 1 2 . Over which interval is the solution valid, and continuous? 2. Solve the equation x 2 y 0 + 2 xy - y 3 = 0 . ( x > 0) 3. Solve the initial value problem y 0 = 2 x ( y + x 2 y ) y (0) = - 2 . 4. Solve the equation (2 x y - y x 2 + y 2 ) dx + ( x x 2 + y 2 - x 2 y 2 ) dy = 0 . 5 . Solve ( x 2 + y 2 ) dy + (3 x 2 y + 2 xy + y 3 )
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Unformatted text preview: . 6. Solve the initial value problem y 00 + 4 y + 5 y = 0 , y (0) = 1 , y (0) = 0 7. Solve the initial value problem 9 y ”-12 y + 4 y = 0 , y (0) = 2 , y (0) =-1 . 8. Solve x 2 y 00 + 4 xy + 2 y = 0 . 9. Solve xy 00-y + 4 x 3 y = 0 , given that y 1 = sin ( x 2 ) is one solution. 1...
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