42.4.5 problem Problem 3.6

Internal problem ID [8833]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.6 Summary and Problems. Page 218
Problem number : Problem 3.6
Date solved : Tuesday, September 30, 2025 at 05:53:07 PM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 33

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

\[ y = \frac {{\mathrm e}^{-2 c_1} x}{\sqrt {-\frac {x^{4} {\mathrm e}^{-4 c_1}}{\operatorname {LambertW}\left (-x^{4} {\mathrm e}^{-4 c_1}\right )}}} \]

✓ Mathematica. Time used: 2.519 (sec). Leaf size: 60

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

\begin{align*} y(x)&\to -\frac {i \sqrt {W\left (-e^{-2 c_1} x^4\right )}}{x}\\ y(x)&\to \frac {i \sqrt {W\left (-e^{-2 c_1} x^4\right )}}{x}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.623 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = x e^{2 C_{1} - \frac {W\left (- x^{4} e^{4 C_{1}}\right )}{2}} \]