32.4.1 problem Recognizable Exact Differential equations. Integrating factors. Example 10.51, page 90

Internal problem ID [5812]
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. Example 10.51, page 90
Date solved : Monday, January 27, 2025 at 01:19:53 PM
CAS classification : [_separable]

\begin{align*} y^{2}+y-x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 13

dsolve((y(x)^2+y(x))-x*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {x}{-x +c_{1}} \]

✓ Solution by Mathematica

Time used: 0.326 (sec). Leaf size: 32

DSolve[(y[x]^2+y[x])-x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {e^{c_1} x}{1-e^{c_1} x} \\ y(x)\to -1 \\ y(x)\to 0 \\ \end{align*}