Question

Solve the differential equation.

dy/dx = xe^(-y)

Answer 1

`(dy)/(dx) = xe^(-y)\ \Rightarrow\ (dy)/(e^(-y) ) = x dx\ \Rightarrow\ \\ \int (dy)/(e^(-y) ) = \int x dx \Rightarrow \int e^y dy= \int x dx \Rightarrow \\ e^y = (x^2)/(2) + C \implies y = \ln\left((x^2)/(2) + C \right)`