Find the general solution for the differential equation:

Question

ex(dy/dx)=e^y-1

Answer 1

Separate variables and integrate both sides:

x dy/dx = e^y

e^-ydy = 1/x dx

-e^-y = ln |x| + C

e^-y = ln |1/x| + C₁

-y = ln (ln |1/x| + C₁)

y = -ln (ln |1/x| + C₁)