Final answer:
The general solution of the differential equation y''-4y'+4y=t^-3/2e^2t includes the complementary solution (C1 + C2t)e^2t and a particular solution found by an appropriate method.
Step-by-step explanation:
The general solution for the differential equation y''-4y'+4y=t-3/2e2t involves finding the complementary solution and the particular solution. To find the complementary solution, we solve the characteristic equation which is associated with the homogeneous part of the given differential equation, r2 - 4r + 4 = 0. As the roots are real and equal, the complementary solution will be of the form (C1 + C2t)e2t. The particular solution can be found using the method of undetermined coefficients. However, since the right-hand side of the equation is a product of a power of t and an exponential function, it may require an extension of the method or the use of variation of parameters.
Without the complete step-by-step solution, it is difficult to provide the exact particular solution. However, once both the complementary and particular solutions are found, they can be combined to give the general solution of the given differential equation.