Hello, rajr!
What methods do you know? . . . . $\displaystyle \begin{array}{c}\text{Undetermined Coefficients?} \\ \text{Variation of Parameters?} \\ \text{Method of Operators?} \end{array}$Find the general solution of the second-order inhomogeneous differential equation:
. . . $\displaystyle y''+3y'+2y\:=\:e^{2x}\cos x$
I have got: .$\displaystyle \lambda \:=\:\text{-}1,\:\text{-}2$
then i got: .$\displaystyle y(x)\:=\:C_1e^{-x}+C_2e^{-2x}$
I am not too sure what to do after this.
can any one check whether my answers are right:
y'' = 2e^(2x)[(2A+B)COSX-(A+2B)SINX]-e^(2x)[(2A+B)SINX + (A+2B)COSX]
AND THEN WHEN I SUBSTITUED THE Y,Y' AND Y'' AND I GOT EQUATIONS AND THEY ARE
13A+7B = 1
-7A-9B = 0
AM I RIGHT..HELP WOULD BE APPRECIATED THANKS