Answer to Question #197876 in Differential Equations for Didues

Question

(D² - 4 ) y = xe^x

Answer 1

Ans:-

$(D^2 - 4 ) y = xe^x$

The Auxiliary equation will be $\ m^2-4=0, \ m=2,2\\$

$C.F.=(Ax+B)e^{2x}$

$P.I.=\dfrac{1}{D^2-4}xe^{x}\\$

$=4e^x (-1+\dfrac{D^2}{4})^{-1}\times x$

$=$$\ \ \ 4e^x$

Hence the complete solution is

$Y=(Ax+B)e^{2x}+4e^x$