I wonder what method to use to solve the following DE: $\displaystyle y'=\frac{1}{e^y -x}$ with the initial condition $\displaystyle y(1)=0$. As a tip they suggest to think of x as a dependent variable of y.

So I'd start with $\displaystyle y'(e^y -x(y))=1$. I don't think it's possible to reduce this DE into a linear one. I'm disoriented. Could you provide the name of a method to solve it? So that I check out my book/Internet and try to solve it alone.

Thanks.