89.31.15 problem 15

Internal problem ID [24960]
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. Exercises at page 246
Problem number : 15
Date solved : Saturday, October 04, 2025 at 06:32:05 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.269 (sec). Leaf size: 5

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

\[ y = 0 \]

✗ Mathematica

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

IndexError : list index out of range