83.41.22 problem 5 (ix)

Internal problem ID [19431]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VIII. Linear equations of second order. Excercise at end of chapter VIII. Page 141
Problem number : 5 (ix)
Date solved : Monday, March 31, 2025 at 07:13:31 PM
CAS classification : [_Gegenbauer, [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 33

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

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

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 45

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

\[ y(x)\to c_1 \cosh \left (m \log \left (\sqrt {x^2-1}+x\right )\right )+i c_2 \sinh \left (m \log \left (\sqrt {x^2-1}+x\right )\right ) \]

✗ Sympy

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

False