I was thinking about the conformal map $w =f(z)$ in which $f$ satisfies $w = f(z) = \frac{df}{dz} - e^z$. Is ths conformal, how can i find the conformal mapping of $z$ plane?
Similarly what will be the case like how it changes if we take $w = f(z) = \int f(z) dz - e^z$?
Seeing the question it hints me to take $f$ as the form of exponential function in $z$ but i ma not getting the equation?
Also hinting to solve the differential equation in real variables and transforming to complex case?