Consider the differential equation: y'' - 6y' + 25y = -t + 4 sin(5t). a. Find the general solution to the corresponding homogeneous equation. In your answer, use c1 and c2 to denote arbitrary constants. Enter c1 as c1 and c2 as c2. y_c = c1e^3t sin(4t) + c2e^3t cos(4t) b. Apply the method of undetermined coefficients to find a particular solution. y_p = A sin(5t) + B cos(5t) c. Solve the initial value problem corresponding to the initial conditions y(0) = 0 and y'(0) = 0. Give your answer as y = . . . . Answer:
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