Find the general solution of the differential equation: $xdy = (e^y - 1)dx$.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $1 - e^{-y} = Cx$ ##
Given differential equation can be written as
$\frac{dy}{dx} = \frac{1}{x}(e^y - 1)$
$\Rightarrow \int \frac{dy}{e^y - 1} = \int \frac{dx}{x}$
$\Rightarrow \int \frac{e^{-y}}{1 - e^{-y}} dy = \int \frac{dx}{x}$
$\Rightarrow \log |1 - e^{-y}| = \log |x| + \log C$
$\Rightarrow 1 - e^{-y} = Cx$