Toronto Math Forum
MAT2442019F => MAT244Test & Quizzes => Quiz1 => Topic started by: Jake Kirbie on September 27, 2019, 02:31:55 PM

Solve the given differential equation:
$$\frac{dy}{dx} = \frac{xe^{x}}{y+e^y}$$
This is a separable differential equation. Rearranging, we have
$$(y+e^y)dy = (xe^{x})dx\ \Rightarrow\ \int(y+e^y)dy = \int(xe^{x})dx\ \Rightarrow\ y^2 + 2e^y = x^2 + 2e^{x} + C$$
is the general implicit solution.