89.31.14 problem 14

Internal problem ID [24959]
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 : 14
Date solved : Thursday, October 02, 2025 at 11:36:38 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

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

✓ Maple. Time used: 0.177 (sec). Leaf size: 607

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

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 139.546 (sec). Leaf size: 8706

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

Too large to display

✓ Sympy. Time used: 98.588 (sec). Leaf size: 923

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

\[ \text {Solution too large to show} \]