60.3.230 problem 1246

Internal problem ID [11226]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1246
Date solved : Sunday, March 30, 2025 at 07:57:36 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Maple. Time used: 0.041 (sec). Leaf size: 28

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

\[ y = \left (\operatorname {hypergeom}\left (\left [\frac {1}{2}, v +1\right ], \left [\frac {3}{2}\right ], x^{2}\right ) c_2 x +c_1 \right ) \left (x^{2}-1\right )^{v} \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 32

ode=-2*v*y[x] - 2*(-1 + v)*x*D[y[x],x] + (-1 + x^2)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \left (x^2-1\right )^{v/2} (c_1 P_v^v(x)+c_2 Q_v^v(x)) \]

✗ Sympy

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

False