23.2.291 problem 310

Internal problem ID [5646]
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 : 310
Date solved : Tuesday, September 30, 2025 at 01:24:04 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} 3 {y^{\prime }}^{3}-x^{4} y^{\prime }+2 x^{3} y&=0 \end{align*}

✓ Maple. Time used: 0.108 (sec). Leaf size: 34

ode:=3*diff(y(x),x)^3-x^4*diff(y(x),x)+2*x^3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {x^{3}}{9} \\ y &= \frac {x^{3}}{9} \\ y &= \frac {c_1^{2} x^{2}-3}{2 c_1^{3}} \\ \end{align*}

✓ Mathematica. Time used: 59.256 (sec). Leaf size: 15992

ode=3 (D[y[x],x])^3 - x^4 D[y[x],x]+2 x^3 y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**4*Derivative(y(x), x) + 2*x**3*y(x) + 3*Derivative(y(x), x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out