23.3.496 problem 502

Internal problem ID [6210]
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 : 502
Date solved : Tuesday, September 30, 2025 at 02:36:23 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

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

\[ y = \frac {c_2 \,x^{3}+c_1}{x^{2}+1} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 26

ode=-2*x*y[x] - 2*(1 - x^2)*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 {c_2 x^3+3 c_1}{3 x^2+3} \end{align*}

✗ Sympy

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

False