23.2.306 problem 327

Internal problem ID [5661]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 327
Date solved : Tuesday, September 30, 2025 at 01:39:25 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: 0.276 (sec). Leaf size: 601

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: 106.25 (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: 100.811 (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)
 

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