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# HW2 - x 5 y 1 = x y 2 = x 2 11 Transform the given equation...

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DIFFERENTIAL EQUATIONS Find a particular solution of the given equation 1. y 00 + y = 2 e x . 2. y 00 - y 0 - y = x + 2 . 3. y 00 - y 0 + y = xe x . Solve the initial value problems 4. y 00 + y = 2 x, y (0) = 1 , y 0 (0) = 2 . 5. y 00 - 3 y 0 + 2 y = e 5 x , y (0) = 0 , y 0 (0) = 3 . 6. y 00 - 2 y 0 + y = 1 + x, y (0) = 3 , y 0 (0) = 0 . Use the method of variation of parameters to find a particular solution of the given equation 7. y 00 - 2 y 0 + y = e 2 x . 8. y 00 - 4 y = e x . 9. x 2 y 00 - 4 xy 0 + 6 y = x 5 , y 1 = x 2 , y 2 = x 3 . 10. x 2 y 00 - 2
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Unformatted text preview: x 5 , y 1 = x, y 2 = x 2 . 11. Transform the given equation into an equivalent system of ﬁrst order differential equations y 00 + 3 y + 2 y = x 2 . 12. Solve the system of differential equations ( u = 2 v, v =-2 u, where u and v are functions of x . 1...
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