Solve y'' - 2y' - y = 0 to get the homogenous solution. This is a second order DE with constant coefficients. y = A e^(1 + sqrt{2})t + B e^(1 - sqrt{2})t.

Get particular solutions for e^(2t) and - e^t. Assume particular solutions of the form a e^(2t) and b e^t. Substitute into DE and solve for a and b.

Add the particular solutions to the homogenous solution to get the general solution.