The goal of this problem is to find the general solution to the linear differential equation...

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The goal of this problem is to find the general solution to the linear differential equation dy dt = 2y + sin(2t). First, observe that the solution y, to the homogeneous part of this differential equation is yn (t) = Ce²t Next, we guess that the solution to the nonhomogeneous equation is yp (t) = A sin (2t) + B cos (2t). Using a Left Hand Side-Right Side Argument, we and B = 0 find that A= 1 So the general solution to the differential equation is y(t) = Ce²t + A sin (2t) + B cos (2t) where A = B = 0 and The goal of this problem is to find the general solution to the linear differential equation dy dt = 2y + sin(2t). First, observe that the solution y, to the homogeneous part of this differential equation is yn (t) = Ce²t Next, we guess that the solution to the nonhomogeneous equation is yp (t) = A sin (2t) + B cos (2t). Using a Left Hand Side-Right Side Argument, we and B = 0 find that A= 1 So the general solution to the differential equation is y(t) = Ce²t + A sin (2t) + B cos (2t) where A = B = 0 and