59.1.66 problem 68

Internal problem ID [9238]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 68
Date solved : Sunday, March 30, 2025 at 02:26:20 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{8}+1\right ) y^{\prime \prime }-16 x^{7} y^{\prime }+72 x^{6} y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 22

ode:=(x^8+1)*diff(diff(y(x),x),x)-16*x^7*diff(y(x),x)+72*x^6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {7}{9} c_1 +c_1 \,x^{8}+c_2 \,x^{9}-\frac {9}{7} c_2 x \]

✗ Mathematica

ode=(1+x^8)*D[y[x],{x,2}]-16*x^7*D[y[x],x]+72*x^6*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-16*x**7*Derivative(y(x), x) + 72*x**6*y(x) + (x**8 + 1)*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False