59.1.474 problem 489

Internal problem ID [9646]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 489
Date solved : Sunday, March 30, 2025 at 02:39:20 PM
CAS classification : [_Gegenbauer]

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-8 x y^{\prime }-12 y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 29

ode:=(-x^2+1)*diff(diff(y(x),x),x)-8*x*diff(y(x),x)-12*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.314 (sec). Leaf size: 73

ode=(1-x^2)*D[y[x],{x,2}]-8*x*D[y[x],x]-12*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {\exp \left (\int _1^x\frac {K[1]+3}{K[1]^2-1}dK[1]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[2]}\frac {K[1]+3}{K[1]^2-1}dK[1]\right )dK[2]+c_1\right )}{\left (x^2-1\right )^2} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*x*Derivative(y(x), x) + (1 - x**2)*Derivative(y(x), (x, 2)) - 12*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False