44.4.11 problem 11

Internal problem ID [9146]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.5. Exact Equations. Page 20
Problem number : 11
Date solved : Tuesday, September 30, 2025 at 06:08:11 PM
CAS classification : [_exact, _rational, _Riccati]

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

✓ Maple. Time used: 0.015 (sec). Leaf size: 24

ode:=y(x)/(1-x^2*y(x)^2)+x/(1-x^2*y(x)^2)*diff(y(x),x) = 1; 
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: 0.096 (sec). Leaf size: 18

ode=y[x]/(1-x^2*y[x]^2)+x/(1-x^2*y[x]^2)*D[y[x],x]==1; 
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: 0.195 (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)
 

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