53.3.13 problem 15

Internal problem ID [8475]
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 : 15
Date solved : Sunday, March 30, 2025 at 01:11:17 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.403 (sec). Leaf size: 36

ode:=y(x) = x^6*diff(y(x),x)^3-x*diff(y(x),x); 
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=y[x]==x^6*(D[y[x],x])^3-x*D[y[x],x]; 
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