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practicemidterm2ODE1

# practicemidterm2ODE1 - (b Find the particular solution...

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Practice Midterm II Professor Cristian Virdol E 1210 November 9, 2009 Name: To receive full credit, you must explain your answers. 1 20 2 20 3 20 4 20 5 20 Total 100 1

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1. (20 points) Find the general solutions of the following differential equa- tions: (a) y (6) + 2 y (4) + y 00 = 0 (b) y (8) + 8 y (4) + 16 y = 0 2
2. (20 points) Find the general solutions of the following differential equations if the method of UNDETERMINED COEFFICIENTS is to be used: (a) y 00 - 4 y 0 + 4 y = 3 t + 5 te 2 t (b) y 00 + y = t 2 + t cos t 3

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3. (20 points) Consider the equation y 00 + 2 y 0 - 8 y = 5 e 3 t (a) Find a particular solution using the method of VARIATION OF PA-

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Unformatted text preview: (b) Find the particular solution satisfying y (0) = 0 and y (0) = 0. 4 4. (20 points) (a) Solve the initial value problem x = ± 2 3 4 5 ² x, x (0) = ± 1 ² (b) Find the general solution of the system: x = ± 2-1 1 4 ² x 5 5. (20 points) Compute W ( y 1 ,y 2 )(10), knowing that y 1 and y 2 are two solu-tions of the diﬀerential equation 2 ty 00 + y + 3 y = 0 satisfying the initial conditions y 1 (1) = 0, y 1 (1) = 1 and y 2 (1) = 1, y 2 (1) = 0. 6...
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practicemidterm2ODE1 - (b Find the particular solution...

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