Internal problem ID [4975]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page
7
Problem number: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\frac {y}{x -1}+\frac {x y^{\prime }}{y+1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 16
dsolve(y(x)/(x-1)+x/(y(x)+1)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {x}{c_{1} x -c_{1}-1} \]
✓ Solution by Mathematica
Time used: 0.281 (sec). Leaf size: 33
DSolve[y[x]/(x-1)+x/(y[x]+1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {e^{c_1} x}{x+e^{c_1} x-1} \\ y(x)\to -1 \\ y(x)\to 0 \\ \end{align*}