Find the general solution of the differential equations `e^xtanydx+(1-e^x)sec^2ydy=0`

Explanation

Integrating the equation, we get
`int (e^(x))/(1-e^(x))dx + int(sec^(2)y)/(tan y)dy = 0`
Put `1-e^(x) = t` for `1^(st)` integral and tan y = u for `2^(nd)` integral
`rArr -e^(x)dx = dt` and `sec^(2) y dy = du`
`rArr int (-dt)/(t) + int(d u)/(u) = 0`
`rArr -In|t| + In|u| = InC`
`rArr u = Ct`
`rArr tan y = C(1-e^(x))`