23.1.25 problem 2(o)

Internal problem ID [4115]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 2. First order equations. Exercises at page 14
Problem number : 2(o)
Date solved : Monday, January 27, 2025 at 08:36:34 AM
CAS classification : [_quadrature]

\begin{align*} x +\left (2-x +2 y\right ) y^{\prime }&=x y \left (y^{\prime }-1\right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

dsolve(x+(2-x+2*y(x))*diff(y(x),x)=x*y(x)*(diff(y(x),x)-1),y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -1 \\ y \left (x \right ) &= x +2 \ln \left (x -2\right )+c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 20

DSolve[x+(2-x+2*y[x])*D[y[x],x]==x*y[x]*(D[y[x],x]-1),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -1 \\ y(x)\to x+2 \log (x-2)+c_1 \\ \end{align*}