4.18 problem Recognizable Exact Differential equations. Integrating factors. Exercise 10.10, page 90

Internal problem ID [3977]

Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 10
Problem number: Recognizable Exact Differential equations. Integrating factors. Exercise 10.10, page 90.
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: 0.015 (sec). Leaf size: 20

dsolve((exp(x)*(x+1))+(y(x)*exp(y(x))-x*exp(x))*diff(y(x),x)=0,y(x), singsol=all)
 

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

Solution by Mathematica

Time used: 0.33 (sec). Leaf size: 26

DSolve[(Exp[x]*(x+1))+(y[x]*Exp[y[x]]-x*Exp[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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