What's the exact value of $y$?

Question

Given that $\frac{dy}{dx}=e^{x-y}$ and $y=1$ when $x=0$ find the exact value of $y$ when $x=1$.

After my attempts. I stuck in $$y=e^{1-y}+1-e^{-1}$$ How to proceed?

Answer 1

A start: Rewrite as $e^y\frac{dy}{dx}=e^x$. This is a separable equation. Integrate. We get $e^y=e^x+C$. Continue.

Answer 2

Your attempted solution is incorrect. Hint: the differential equation $\dfrac{dy}{dx} = e^{x-y}$ is separable.