12.1.15 problem 5(d)

Internal problem ID [1533]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 1, Introduction. Section 1.2 Page 14
Problem number : 5(d)
Date solved : Monday, January 27, 2025 at 04:59:06 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.042 (sec). Leaf size: 11

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

\[ y = \frac {2}{x -2} \]

✓ Solution by Mathematica

Time used: 0.220 (sec). Leaf size: 12

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

\[ y(x)\to \frac {2}{x-2} \]