# Answer to Question #17051 in Differential Equations for arif

Question #17051

find solution of separable ODE

3e^xtanydx+(1-e^x)sec^ydy=0

3e^xtanydx+(1-e^x)sec^ydy=0

Expert's answer

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)

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)

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