# Linear differential equations and IVP

Hey I'm currently stuck on this question. I don't think its in the form of an integrating factor, but I'm also not sure if its separable?

$$\frac {dy}{dx}=-3y+2e^{-x}$$

The general form for an equation solvable by integrating factor is $$\frac{dy}{dx}+P(x)y=Q(x).$$
In your case I see $$\frac{dy}{dx}+3y=2e^{-x}.$$
• How about $P(x)=3x^0$. There is your $x$ term. ;). Not to be a smarty pants, just think of $P(x)$ as being $P(x)=3$. – J. W. Perry Sep 19 '14 at 5:48
• Oh i see that now! Could you tell me if I'm correct, where the integrating factor is: $$e^{3x+c}$$ or simplified to be $$e^{3x}$$ – user176330 Sep 19 '14 at 5:58
• If your have $\mu(x)=e^{\int 3\, dx }$ then you are correct. – J. W. Perry Sep 19 '14 at 6:01