2. Consider the ODE y00 + 2y0 + 2y = g(t). (a) Find the homogeneous solution of the ODE. (b) If g(t) = 1 − t2 + 5 cos 2t

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2. Consider the ODE y00 + 2y0 + 2y = g(t).
(a) Find the homogeneous solution of the ODE.
(b) If g(t) = 1 − t2 + 5 cos 2t, find the particular solution using the method of undetermined
coefficients. Compute all coefficients explicitly.
(c) Write down the general solution of the problem.
(d) Write down the correct form of the particular solution if g(t) = 2e
−t sin t. You don’t need
to compute the coefficients.