53.3.14 problem 16

Internal problem ID [8476]
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 : 16
Date solved : Sunday, March 30, 2025 at 01:11:31 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} x {y^{\prime }}^{4}-2 y {y^{\prime }}^{3}+12 x^{3}&=0 \end{align*}

✓ Maple. Time used: 0.369 (sec). Leaf size: 66

ode:=x*diff(y(x),x)^4-2*y(x)*diff(y(x),x)^3+12*x^3 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {2 \sqrt {6}\, \left (-x \right )^{{3}/{2}}}{3} \\ y &= -\frac {2 \sqrt {6}\, \left (-x \right )^{{3}/{2}}}{3} \\ y &= -\frac {2 \sqrt {6}\, x^{{3}/{2}}}{3} \\ y &= \frac {2 \sqrt {6}\, x^{{3}/{2}}}{3} \\ y &= \frac {12 c_1^{4}+x^{2}}{2 c_1} \\ \end{align*}

✓ Mathematica. Time used: 133.223 (sec). Leaf size: 30947

ode=x*(D[y[x],x])^4-2*y[x]*(D[y[x],x])^3+12*x^3==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(12*x**3 + x*Derivative(y(x), x)**4 - 2*y(x)*Derivative(y(x), x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out