60.3.227 problem 1243

Internal problem ID [11223]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1243
Date solved : Wednesday, March 05, 2025 at 01:56:58 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.043 (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]
 

\[ y(x)\to \frac {e^{-i x} \left (2 c_1-i c_2 e^{2 i x}\right )}{2 \left (x^2-1\right )} \]

✗ Sympy

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

False