M2 Review Problems

# B find the general solution to the diﬀerential

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(b) Find the general solution to the diﬀerential equation. Identify the fundamental set for solutions to the corresponding homogeneous equation and the particular solution to the nonhomogeneous equation that appears in your general solution. (c) Find a diﬀerent fundamental set for solutions to the homogeneous equation and a diﬀerent particular solution and express the general solution in terms of these functions. (d) Solve the DE with initial conditions y (0) = 2 and y 0 (0) = 0. 10. Solve IVP: y 00 + 2 y 0 + y = 2 e - t , y (0) = 1 , y 0 (0) = 0 . 11. Solve IVP: y 00 + 2 y 0 + 5 y = 4 e - t cos(2 t ) , y (0) = 1 , y 0 (0) = 0 . 12. In each of the following problems (1) verify that the given functions y 1 and y 2 are solutions to the associated homogeneous equation, then (2) use Variation of Parameters to ﬁnd the general solution of the given nonhomogeneous equation. 4

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