76.4.22 problem 28

Internal problem ID [17416]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.6 (Exact equations and integrating factors). Problems at page 100
Problem number : 28
Date solved : Tuesday, January 28, 2025 at 10:06:28 AM
CAS classification : [[_1st_order, _with_exponential_symmetries]]

\begin{align*} y+\left (2 y x -{\mathrm e}^{-2 y}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.676 (sec). Leaf size: 24

dsolve(y(x)+ (2*x*y(x)-exp(-2*y(x)))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (c_{1} {\mathrm e}^{-2 \,{\mathrm e}^{\textit {\_Z}}}+\textit {\_Z} \,{\mathrm e}^{-2 \,{\mathrm e}^{\textit {\_Z}}}-x \right )} \]

✓ Solution by Mathematica

Time used: 0.263 (sec). Leaf size: 25

DSolve[y[x]+(2*x*y[x]-Exp[-2*y[x]])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x=e^{-2 y(x)} \log (y(x))+c_1 e^{-2 y(x)},y(x)\right ] \]