23.3.492 problem 498

Internal problem ID [6206]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 498
Date solved : Tuesday, September 30, 2025 at 02:36:19 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x^{3}-y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

ode:=x^3-diff(y(x),x)+x*(-x^2+1)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{2}}{2}+c_1 \sqrt {x -1}\, \sqrt {x +1}+c_2 \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 30

ode=x^3 - D[y[x],x] + x*(1 - x^2)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^2}{2}-c_1 \sqrt {1-x^2}+c_2 \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3 + x*(1 - x**2)*Derivative(y(x), (x, 2)) - Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out