Question

Differential equations dy/dx = e^x-y

Answer 1

$\frac{dy}{dx}=e^{x-y} \\ \\ \frac{dy}{dx}=\frac{e^{x}}{e^{y}} \\ \\ e^{y} \text{ } dy=e^{x} \text{ } dx \\ \\ \int e^{y} \text{ } dy=\int e^{x} \text{ } dx \\ \\ e^{y}=e^{x}+C \\ \\ \boxed{y=\ln \left(e^{x}+C \right)}$