Toronto Math Forum

MAT244--2019F => MAT244--Test & Quizzes => Quiz-1 => Topic started by: Yichen Ji on November 04, 2019, 05:58:57 PM

Title: TUT 0602 Quiz 1
Post by: Yichen Ji on November 04, 2019, 05:58:57 PM
Question:Solve the given differential equation:
\begin{equation*}
    \frac{dy}{dx}=\frac{x-e^{-x}}{y+e^{y}}
\end{equation*}
Solution:
Reordering:
\begin{equation*}
    (y+e^{y})dy=(x-e^{-x})dx
\end{equation*}
Take integration and multiplying$2$on both sides:
\begin{equation*}
    y^2+2e^{y}=x^2+2e^{-x}+c
\end{equation*}
for $c$ being constant.
Reordering,get implicit solution
\begin{equation*}
    y^2-x^2+2e^{y}-2e{-x}=c
\end{equation*}