Internal problem ID [2624]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, End of chapter, page 61
Problem number: 25.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {\left (x +1\right ) {\mathrm e}^{x}-\left ({\mathrm e}^{x} x -{\mathrm e}^{y} y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (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)
\[ x \,{\mathrm e}^{-y \relax (x )+x}+\frac {y \relax (x )^{2}}{2}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.329 (sec). Leaf size: 26
DSolve[Exp[x]*(1+x)==(x*Exp[x]-y[x]*Exp[y[x]])*y'[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {1}{2} y(x)^2-x e^{x-y(x)}=c_1,y(x)\right ] \]