20.2.11 problem 11

Internal problem ID [4260]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, section 8, page 41
Problem number : 11
Date solved : Tuesday, September 30, 2025 at 07:11:09 AM
CAS classification : [_exact, _rational, _Riccati]

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

✓ Maple. Time used: 0.014 (sec). Leaf size: 24

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

\[ y = \frac {c_1 +{\mathrm e}^{2 x}}{x \left ({\mathrm e}^{2 x}-c_1 \right )} \]

✓ Mathematica. Time used: 0.107 (sec). Leaf size: 18

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

\begin{align*} y(x)&\to \frac {\tanh (x+i c_1)}{x} \end{align*}

✓ Sympy. Time used: 0.255 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = \frac {- C_{1} - e^{2 x}}{x \left (C_{1} - e^{2 x}\right )} \]