89.30.12 problem 14

Internal problem ID [24929]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 16. Equations of order one and higher degree. Exercises at page 243
Problem number : 14
Date solved : Thursday, October 02, 2025 at 10:49:49 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.131 (sec). Leaf size: 32

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

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

✓ Mathematica. Time used: 131.975 (sec). Leaf size: 24834

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

Too large to display

✗ Sympy

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

Timed Out