29.24.1 problem 663

Internal problem ID [5254]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 24
Problem number : 663
Date solved : Sunday, March 30, 2025 at 07:31:51 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} \left (1-x^{2} y^{2}\right ) y^{\prime }&=x y^{3} \end{align*}

✓ Maple. Time used: 0.039 (sec). Leaf size: 32

ode:=(1-x^2*y(x)^2)*diff(y(x),x) = x*y(x)^3; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 4.069 (sec). Leaf size: 60

ode=(1-x^2 y[x]^2)D[y[x],x]==x y[x]^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.917 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*y(x)**3 + (-x**2*y(x)**2 + 1)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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