59.1.647 problem 664

Internal problem ID [9819]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 664
Date solved : Sunday, March 30, 2025 at 02:47:19 PM
CAS classification : [_Gegenbauer]

\begin{align*} \left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y&=0 \end{align*}

✓ Maple. Time used: 0.028 (sec). Leaf size: 48

ode:=(-4*x^2+1)*diff(diff(y(x),x),x)-20*x*diff(y(x),x)-16*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {2 \ln \left (2 x +\sqrt {4 x^{2}-1}\right ) c_2 x -\sqrt {4 x^{2}-1}\, c_2 +c_1 x}{\left (4 x^{2}-1\right )^{{3}/{2}}} \]

✓ Mathematica. Time used: 0.101 (sec). Leaf size: 57

ode=(1-4*x^2)*D[y[x],{x,2}]-20*x*D[y[x],x]-16*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {-2 c_2 x \arcsin (2 x)-c_2 \sqrt {1-4 x^2}+c_1 x}{\sqrt [4]{1-4 x^2} \left (4 x^2-1\right )^{5/4}} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-20*x*Derivative(y(x), x) + (1 - 4*x**2)*Derivative(y(x), (x, 2)) - 16*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False