78.5.8 problem 2 (h)

Internal problem ID [18151]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 9 (Integrating Factors). Problems at page 80
Problem number : 2 (h)
Date solved : Tuesday, January 28, 2025 at 11:34:14 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: 0.022 (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: 0.229 (sec). Leaf size: 32

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

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