Answer to Question #17051 in Differential Equations for arif

Question

find solution of separable ODE
3e^xtanydx+(1-e^x)sec^ydy=0

Answer 1

we can rewrite it as
3e^xtanydx=(e^x-1)sec^ydy
3*e^x/(e^x-1)
dx=sec(y)/tan(y) dy
integrate and we get
3
log(1-e^x)+c=ln(tan(y))
y=arctan( c1*(1-e^x)^3)