1. ## Diferential equations

Find the general solution of the second-order inhomogeneous differential equation

y''+3y'+2y=

I have got lamda equals to -2 and -1 and then i got

y(x)=Ae^(-2x)+Be^(-2x)

I am not too sure what to do after this.. help would be appreciated thx

2. Hello, rajr!

Find the general solution of the second-order inhomogeneous differential equation:

. . . $y''+3y'+2y\:=\:e^{2x}\cos x$

I have got: . $\lambda \:=\:\text{-}1,\:\text{-}2$

then i got: . $y(x)\:=\:C_1e^{-x}+C_2e^{-2x}$

I am not too sure what to do after this.
What methods do you know? . . . . $\begin{array}{c}\text{Undetermined Coefficients?} \\ \text{Variation of Parameters?} \\ \text{Method of Operators?} \end{array}$

3. undetermined coefficients

4. Originally Posted by rajr
Find the general solution of the second-order inhomogeneous differential equation

y''+3y'+2y=

I have got lamda equals to -2 and -1 and then i got

y(x)=Ae^(-2x)+Be^(-2x)

I am not too sure what to do after this.. help would be appreciated thx
Try y(x)= $e^{2x}(C cos(x)+ D sin(x))$

5. i have to find y' and y'' for this right!

6. i got y' to be A (2e^(2x)sin(x))+a (e^(2x)cox(x))+B(2e^(2x)cosx)-B(sinxe^(2x))

7. Originally Posted by rajr
i got y' to be A (2e^(2x)sin(x))+a (e^(2x)cox(x))+B(2e^(2x)cosx)-B(sinxe^(2x))
I think it is simpler not to multiply it out. If $y= e^{2x}(A cos(x)+ B sin(x))$ then $y'= 2e^{2x}(A cos(x)+ B sin(x))+ e^{2x}(-A sin(x)+ B cos(x))$

8. ## Can some one check my solution

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