67.3.47 problem 4.8 (f)

Internal problem ID [16368]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.8 (f)
Date solved : Thursday, October 02, 2025 at 01:22:46 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {-1+y^{2}}{y x} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.063 (sec). Leaf size: 15

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

\[ y = -\sqrt {3 x^{2}+1} \]

✓ Mathematica. Time used: 0.187 (sec). Leaf size: 18

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

\begin{align*} y(x)&\to -\sqrt {3 x^2+1} \end{align*}

✓ Sympy. Time used: 0.249 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = - \sqrt {3 x^{2} + 1} \]