29.24.10 problem 672

Internal problem ID [5263]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 24
Problem number : 672
Date solved : Sunday, March 30, 2025 at 07:33:18 AM
CAS classification : [_separable]

\begin{align*} x^{3} \left (1+y^{2}\right ) y^{\prime }+3 x^{2} y&=0 \end{align*}

✓ Maple. Time used: 0.015 (sec). Leaf size: 33

ode:=x^3*(1+y(x)^2)*diff(y(x),x)+3*x^2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{-3 c_1}}{\sqrt {\frac {{\mathrm e}^{-6 c_1}}{x^{6} \operatorname {LambertW}\left (\frac {{\mathrm e}^{-6 c_1}}{x^{6}}\right )}}\, x^{3}} \]

✓ Mathematica. Time used: 3.424 (sec). Leaf size: 46

ode=x^3(1+y[x]^2)D[y[x],x]+3 x^2 y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\sqrt {W\left (\frac {e^{2 c_1}}{x^6}\right )} \\ y(x)\to \sqrt {W\left (\frac {e^{2 c_1}}{x^6}\right )} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.754 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = \frac {e^{C_{1} - \frac {W\left (\frac {e^{2 C_{1}}}{x^{6}}\right )}{2}}}{x^{3}} \]