Solving Particular Integral of Polynomial & Exponential

[enosthapa]

y''+5y'+4y=x^2+2e^(-x)
Auxiliary roots: m1=-1 m2=-4

Using trial please
cant seem to work out PI with polynomial and exponential together.

 

[tiny-tim]

hi enosthapa!

(try using the X² icon just above the Reply box )

when your RHS contains an exponential which is a solution of the LHS, it obviously can't be a PI on its own (as you've found out! ) …

you need to multiply it by x (or xⁿ is it's an nth root of the LHS) …

in this case, try xe^-x (plus a polynomial) ​

 

[enosthapa]

Thanks a lot but I am still confused
As far as i know,
if there is exponential on RHS (e^kx) and if 'k' is simple root of the auxiliary equation which it is in this case, then we try a.x.e^k.x i.e a.x.e^-x

but the question has polynomial in addition so did you mean i have to add the 'PI' I would get if there was polynomial only on RHS?
sorry i m confusing u:/

 

[tiny-tim]

i meant a polynomial plus a constant times xe^-x …

doesn't that work? ​

 

[enosthapa]

I don't have the answer which could have been helpful. But thanks anyway.

 

[Redbelly98]

Moderator's note: thread moved from "Differential Equations".

The usual rules rules for giving homework help are now in effect.