25.2.3 problem 3

Internal problem ID [6859]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 3
Problem number : 3
Date solved : Tuesday, September 30, 2025 at 03:56:05 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} \frac {3 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 22

ode:=3*x/y(x)^3+(1/y(x)^2-3*x^2/y(x)^4)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sqrt {3}\, \sqrt {-\frac {1}{\operatorname {LambertW}\left (-3 c_1 \,x^{2}\right )}}\, x \]

✓ Mathematica. Time used: 7.093 (sec). Leaf size: 70

ode=(3*x/y[x]^3)+(1/y[x]^2-3*x^2/y[x]^4)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {i \sqrt {3} x}{\sqrt {W\left (-3 e^{-3-2 c_1} x^2\right )}}\\ y(x)&\to \frac {i \sqrt {3} x}{\sqrt {W\left (-3 e^{-3-2 c_1} x^2\right )}}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.802 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x/y(x)**3 + (-3*x**2/y(x)**4 + y(x)**(-2))*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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