47.1.15 problem 15

Internal problem ID [7396]
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
Date solved : Monday, January 27, 2025 at 02:52:04 PM
CAS classification : [_separable]

\begin{align*} \frac {y}{x -1}+\frac {x y^{\prime }}{y+1}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.543 (sec). Leaf size: 33

DSolve[y[x]/(x-1)+x/(y[x]+1)*D[y[x],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*}