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

Internal problem ID [5829]
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
Date solved : Monday, January 27, 2025 at 01:20:09 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} {\mathrm e}^{x} \left (1+x \right )+\left (y \,{\mathrm e}^{y}-x \,{\mathrm e}^{x}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.009 (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)
 

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

✓ Solution by Mathematica

Time used: 0.300 (sec). Leaf size: 26

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

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