Question

Find the P.I of (D2 + 2D + 1)y = e-X​

Answer 1

Answer:

Here yC.F. = c1ex + c2xex Since the right hand member of the complete equation is Xx = ex therefore the first possible assumption for particular integral would be yP.I. = Aex but this solution has already occurred in yC.F. We therefore yP.I.x = Axex. Still this solution also has appeared in yC.F. We therefore again multiply by x and try yP.I.x = Ax2ex.