Internal problem ID [3960]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{2}+y-x y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 13
dsolve((y(x)^2+y(x))-x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {x}{c_{1}-x} \]
✓ Solution by Mathematica
Time used: 0.256 (sec). Leaf size: 28
DSolve[(y[x]^2+y[x])-x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -1+\frac {1}{1-e^{c_1} x} \\ y(x)\to -1 \\ y(x)\to 0 \\ \end{align*}