What is a general solution to the differential equation #dy/dx=xe^-y#?

Question

2666 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-19T08:15:24

This is a separable differential equation.

#dy/(dx) = xe^(-y)#

#dy/(dx) = x*1/(e^y) #

#e^y * dy/(dx) = x#

#e^y dy = x dx#

#int e^y dy = int x dx#

#e^y = 1/2 x^2 + C#

#y = ln(1/2 x^2+C)#