40.3.31 problem 26 (e)

Internal problem ID [6635]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 26 (e)
Date solved : Sunday, March 30, 2025 at 11:13:00 AM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Maple. Time used: 0.017 (sec). Leaf size: 38

ode:=3*y(x)^3-x*y(x)-(x^2+6*x*y(x)^2)*diff(y(x),x) = 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: 3.447 (sec). Leaf size: 73

ode=(3*y[x]^3-x*y[x])-(x^2+6*x*y[x]^2)*D[y[x],x]==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: 9.191 (sec). Leaf size: 24

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

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