23.3.370 problem 374

Internal problem ID [6084]
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 : 374
Date solved : Tuesday, September 30, 2025 at 02:21:12 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} -\left (x^{2}+1\right ) y-4 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 21

ode:=-(x^2+1)*y(x)-4*x*diff(y(x),x)+(-x^2+1)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \sin \left (x \right )+c_2 \cos \left (x \right )}{x^{2}-1} \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 41

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x*Derivative(y(x), x) + (1 - x**2)*Derivative(y(x), (x, 2)) + (-x**2 - 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False