53.3.19 problem 22

Internal problem ID [8481]
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 : 22
Date solved : Sunday, March 30, 2025 at 01:11:40 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

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

✓ Maple. Time used: 0.032 (sec). Leaf size: 141

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

\begin{align*} y &= \frac {2 \left (\sqrt {x^{2}+3 c_1}-2 x \right ) \sqrt {-6 \sqrt {x^{2}+3 c_1}-6 x}}{9} \\ y &= -\frac {2 \left (\sqrt {x^{2}+3 c_1}-2 x \right ) \sqrt {-6 \sqrt {x^{2}+3 c_1}-6 x}}{9} \\ y &= -\frac {2 \left (\sqrt {x^{2}+3 c_1}+2 x \right ) \sqrt {6 \sqrt {x^{2}+3 c_1}-6 x}}{9} \\ y &= \frac {2 \left (\sqrt {x^{2}+3 c_1}+2 x \right ) \sqrt {6 \sqrt {x^{2}+3 c_1}-6 x}}{9} \\ \end{align*}

✗ Mathematica

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

Timed out

✗ Sympy

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

Timed Out