78.8.25 problem 25

Internal problem ID [18223]
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. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 25
Date solved : Tuesday, January 28, 2025 at 11:40:41 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} \left (1+x \right ) {\mathrm e}^{x}&=\left (x \,{\mathrm e}^{x}-y \,{\mathrm e}^{y}\right ) y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 20

dsolve(exp(x)*(1+x)=(x*exp(x)-y(x)*exp(y(x)))*diff(y(x),x),y(x), singsol=all)
 

\[ x \,{\mathrm e}^{x -y}+\frac {y^{2}}{2}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.342 (sec). Leaf size: 26

DSolve[Exp[x]*(1+x)==(x*Exp[x]-y[x]*Exp[y[x]])*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [-\frac {1}{2} y(x)^2-x e^{x-y(x)}=c_1,y(x)\right ] \]