29.36.7 problem 1071

Internal problem ID [5634]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 36
Problem number : 1071
Date solved : Sunday, March 30, 2025 at 09:34:47 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} x^{6} {y^{\prime }}^{3}-x y^{\prime }-y&=0 \end{align*}

✓ Maple. Time used: 0.490 (sec). Leaf size: 36

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

\begin{align*} y &= -\frac {2 \sqrt {3}}{9 x^{{3}/{2}}} \\ y &= \frac {2 \sqrt {3}}{9 x^{{3}/{2}}} \\ y &= c_1^{3}-\frac {c_1}{x} \\ \end{align*}

✗ Mathematica

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

Timed out

✗ Sympy

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

Timed Out