23.3.543 problem 549

Internal problem ID [6257]
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 : 549
Date solved : Tuesday, September 30, 2025 at 02:39:03 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

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

\[ y = x \left (c_1 +c_2 \ln \left (x +\sqrt {x^{2}-1}\right )\right ) \]

✓ Mathematica. Time used: 0.044 (sec). Leaf size: 45

ode=(2 - x^2)*y[x] - x*(2 - x^2)*D[y[x],x] + x^2*(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 \sqrt [4]{x^2-1} \left (c_2 \log \left (\sqrt {x^2-1}+x\right )+c_1\right )}{\sqrt [4]{1-x^2}} \end{align*}

✗ Sympy

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

False