Toronto Math Forum

MAT244--2019F => MAT244--Test & Quizzes => Quiz-1 => Topic started by: Jake Kirbie on September 27, 2019, 02:31:55 PM

Title: Q1: TUT0602
Post by: Jake Kirbie on September 27, 2019, 02:31:55 PM
Solve the given differential equation:

$$\frac{dy}{dx} = \frac{x-e^{-x}}{y+e^y}$$

This is a separable differential equation. Rearranging, we have

$$(y+e^y)dy = (x-e^{-x})dx\ \Rightarrow\ \int(y+e^y)dy = \int(x-e^{-x})dx\ \Rightarrow\ y^2 + 2e^y = x^2 + 2e^{-x} + C$$

is the general implicit solution.