How to find Particular integral of this differential eq:

[abrowaqas]

Homework Statement

Solve the following differential equation

y'''-3y''+2y' = e^x/(1+e^(-x))

Homework Equations

The Attempt at a Solution

first i find the complementary function i-e
Yc= C1 e^x + C2 e^(1+√3)x + C3 (1-√3)x

now i started to find particular integral by

Yp = 1/f(D) e^x/(1+e^(-x))
= e^x 1/f(D+1) 1 /(1+e^(-x))
= e^x 1/f(D+1) e^x/e^x+1

i am stuch here... how i may go now..

can anybody tell me how i find Particular Integral of this question?

 

[LCKurtz]

I think your complementary solution is wrong. The roots of your characteristic equation are 0,1, and 2. Once you fix that you will need to use variation of parameters to get a particular solution of the NH equation.

 

[abrowaqas]

oh yes... thanks LCKurtz..
but Variation of Parameters taking too long..
do you have any other method to solve it..

 

[LCKurtz]

oh yes... thanks LCKurtz..
but Variation of Parameters taking too long..
do you have any other method to solve it..

Maple.