Solution of $\frac{dy}{dx}=2^{y-x}$ is :

$2^{-y}+2^{-x}=k$ $2^{-y}=k-3.2^{-x}$ $2^{-y}-2^{-x}=k$ $2^{-y}-5.2^{-x}=k$

$2^{-y}-2^{-x}=k$