26.5.20 problem 25

Internal problem ID [4294]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, End of chapter, page 61
Problem number : 25
Date solved : Monday, January 27, 2025 at 08:50:04 AM
CAS classification : [`y=_G(x,y')`]

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

✓ Solution by Maple

Time used: 0.010 (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)
 

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

✓ Solution by Mathematica

Time used: 0.314 (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]
 

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