6.1.15 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 : Tuesday, September 30, 2025 at 04:35:29 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*}

✓ Maple. Time used: 0.030 (sec). Leaf size: 11

ode:=diff(y(x),x) = -y(x)*(y(x)+1)/x; 
ic:=[y(1) = -2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.148 (sec). Leaf size: 12

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

\begin{align*} y(x)&\to \frac {2}{x-2} \end{align*}

✓ Sympy. Time used: 0.158 (sec). Leaf size: 7

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) + (y(x) + 1)*y(x)/x,0) 
ics = {y(1): -2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {2}{x - 2} \]