73.3.47 problem 4.8 (f)

Internal problem ID [15002]
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, March 13, 2025 at 05:26:19 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.033 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.277 (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]
 

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

✓ Sympy. Time used: 0.402 (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)
 

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