Solve the initial value problem explicity:

Question

y'= 5xe^(-y), y(1)=1

Answer 1

This equation is separable:
y'/(5e^(-y)) = x
Integrate and substitute y(1)=1 to solve for the integration constant C.
See solution to your other post for reference:
http://www.jiskha.com/display.cgi?id=1296694049