53.3.12 problem 14

Internal problem ID [8474]
Book : Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam Publishing Co. NY. 6th edition. 1981.
Section : CHAPTER 16. Nonlinear equations. Section 99. Clairaut equation. EXERCISES Page 320
Problem number : 14
Date solved : Sunday, March 30, 2025 at 01:11:06 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: 0.220 (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: 123.852 (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