Question

Solve (D² – 2D + 1)y = e^x by method of undetermined coefficients.

Answer 1

Here y_C.F. = c₁e^x + c₂xe^x Since the right hand member of the complete equation is X(x) = e^x, therefore the first possible assumption for particular integral would be y_P.I. = Ae^x, but this solution has already occurred in y_C.F. We, therefore, y_P.I.(x) = Axe^x. Still this solution also has appeared in y_C.F. We, therefore, again multiply by x and try y_P.I.(x) = Ax²e^x.