Suppose the functions y1 t e2t and y2 t e2t span the solut

Suppose the functions y_1 (t) = e^-2t and y_2 (t) = e^2t span the solution space for the homogeneous linear DE: L(y) = 0 Specify the form of the solution to the non-homogeneous equation L(y) = e^2t

Solution

Since e^{2t} is already a solution to homogeneous ode so the guess for particular solution is

yp=Cte^{2t}

HEnce form of general solutoin is

y=Ae^{-2t}+Be^{2t}+Cte^{2t}