89.32.15 problem 17

Internal problem ID [24975]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 16. Equations of order one and higher degree. Miscellaneous Exercises at page 246
Problem number : 17
Date solved : Thursday, October 02, 2025 at 11:45:14 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: 0.012 (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