Sorry about the influx of my threads; panicking slightly about my distinct lack of ability when it comes to differential equations. I have the equation...

$\displaystyle y''+y'-2y=0$ with $\displaystyle y\rightarrow 0$ as $\displaystyle x\rightarrow +\infty$ and $\displaystyle y(0)=2$

I got the auxilliary equation $\displaystyle \lambda^2+\lambda -2=0$ and factorised to get $\displaystyle \lambda_1=-2 ; \lambda_2=1$, so the general solution is...

$\displaystyle y=Ae^{-2x}+Be^{x}$

But I don't know how to find A and B with those conditions

I get $\displaystyle A+B=2$ but that's about as far as I got. Any ideas?