76.4.17 problem 21

Internal problem ID [17411]
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 : 21
Date solved : Tuesday, January 28, 2025 at 10:06:19 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Solution by Maple

Time used: 0.273 (sec). Leaf size: 34

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

\[ \frac {\left (-y^{2}+2 y-2\right ) {\mathrm e}^{y}+x y^{2}-c_{1}}{y^{2}} = 0 \]

✓ Solution by Mathematica

Time used: 0.219 (sec). Leaf size: 32

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

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