Solving Exponential PDE

Question

Can anyone help me solve this? I am having a hard time figuring this out.

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

Answer 1

Hint $$\frac{d}{dx}\left(e^{-x}y\right)=1$$

Answer 2

The equation $\frac{dy}{dx}=e^x+y$ can be rewritten as $\frac{dy}{dx}+P(x)y=Q(x)$ where $P(x)=-1$ and $Q(x)=e^x$. The general solution for $y$ can then be found through the well known method of integrating factors.

Answer 3

Hint

Let $y=z\, e^x$ to get $z'=1$