32.6.33 problem Exercise 12.33, page 103

Internal problem ID [5898]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.33, page 103
Date solved : Sunday, March 30, 2025 at 10:24:28 AM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} \left (x^{2} y-1\right ) y^{\prime }+x y^{2}-1&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 51

ode:=(x^2*y(x)-1)*diff(y(x),x)+x*y(x)^2-1 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {1+\sqrt {-2 c_1 \,x^{2}+2 x^{3}+1}}{x^{2}} \\ y &= \frac {1-\sqrt {-2 c_1 \,x^{2}+2 x^{3}+1}}{x^{2}} \\ \end{align*}

✓ Mathematica. Time used: 0.627 (sec). Leaf size: 57

ode=(x^2*y[x]-1)*D[y[x],x]+x*y[x]^2-1==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {1-\sqrt {2 x^3+c_1 x^2+1}}{x^2} \\ y(x)\to \frac {1+\sqrt {2 x^3+c_1 x^2+1}}{x^2} \\ \end{align*}

✗ Sympy

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

Timed Out