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Mat 262 Exam-2 - 3 4 2sin y y y t ′′ ′-= 6 Solve the...

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Mat 262 Exam 2 Name SHOW ALLWORK Date 06/10/09 1. Determine whether the given functions are linearly independent on the interval ( 29 , -∞ ∞ . ( 29 1 x f x e = , ( 29 2 x f x xe = , ( 29 2 3 x f x x e = 2. Verify that the given two – parameter family of functions is the general solution of the non – homogeneous differential equation on the indicated interval. 7 10 24 x y y y e ′′ - + = , such that 2 5 1 2 6 x x x y c e c e e = + + on the interval ( 29 , -∞ ∞
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3. Find a second solution of each differential equation. Formula: ( 29 ( 29 ( 29 2 1 2 1 P x dx e y y x dx y x - = Given: ( 29 2 0 xy x y ′′ - + = ; ( 29 1 1 y x =
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4. Find the general solution of the given differential equation. a. 3 2 3 2 3 5 10 4 0 d y d y dy y dx dx dx + + - = b. 2 3 4 0 y y y - + = && & c. 3 2 3 2 12 36 0 d y d y dy dx dx dx + + =
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5. Solve the differential equation by the method of undetermined coefficients.
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Unformatted text preview: 3 4 2sin y y y t ′′ ′--= 6. Solve the differential equation by variation of parameters. 9 9 x x y y e ′′ -= Formula: 2 1 1 2 y f u W y f u W ′ = - ′ = 7. Solve the Cauchy-Euler Equations. a. 2 2 x y xy y ′′ ′ + + = b. 2 5 4 x y xy y ′′ ′ + + = 8. A force of 400 Newton’s stretches a spring 2 m. A mass of 50 kg is attached to the end of the spring and released from equilibrium position with an upward velocity of 10 m s . Find the equation of motion and ivp’s (DO NOT SOLVE)...
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