29.23.28 problem 659

Internal problem ID [5250]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 23
Problem number : 659
Date solved : Sunday, March 30, 2025 at 07:31:04 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} x \left (x +6 y^{2}\right ) y^{\prime }+x y-3 y^{3}&=0 \end{align*}

✓ Maple. Time used: 0.078 (sec). Leaf size: 38

ode:=x*(x+6*y(x)^2)*diff(y(x),x)+x*y(x)-3*y(x)^3 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{\frac {3 c_1}{2}} \sqrt {6}}{6 x \sqrt {\frac {{\mathrm e}^{3 c_1}}{x^{3} \operatorname {LambertW}\left (\frac {6 \,{\mathrm e}^{3 c_1}}{x^{3}}\right )}}} \]

✓ Mathematica. Time used: 3.445 (sec). Leaf size: 73

ode=x(x+6 y[x]^2)D[y[x],x]+x y[x]-3 y[x]^3==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{2+3 c_1}}{x^3}\right )}}{\sqrt {6}} \\ y(x)\to \frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{2+3 c_1}}{x^3}\right )}}{\sqrt {6}} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 10.195 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(x + 6*y(x)**2)*Derivative(y(x), x) + x*y(x) - 3*y(x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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