53.3.3 problem 5

Internal problem ID [8465]
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 : 5
Date solved : Sunday, March 30, 2025 at 01:08:39 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} 2 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+x^{4}&=0 \end{align*}

✓ Maple. Time used: 0.370 (sec). Leaf size: 54

ode:=2*x*diff(y(x),x)^3-6*y(x)*diff(y(x),x)^2+x^4 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {\left (1+i \sqrt {3}\right ) x^{2}}{4} \\ y &= \frac {\left (i \sqrt {3}-1\right ) x^{2}}{4} \\ y &= \frac {x^{2}}{2} \\ y &= \frac {1}{6 c_1^{2}}+\frac {c_1 \,x^{3}}{3} \\ \end{align*}

✓ Mathematica. Time used: 152.887 (sec). Leaf size: 21360

ode=2*x*(D[y[x],x])^3-6*y[x]*(D[y[x],x])^2+x^4==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(x**4 + 2*x*Derivative(y(x), x)**3 - 6*y(x)*Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out