59.1.163 problem 165

Internal problem ID [9335]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 165
Date solved : Sunday, March 30, 2025 at 02:32:38 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 9 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+3 x \left (13 x^{2}+7 x +1\right ) y^{\prime }+\left (25 x^{2}+4 x +1\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 22

ode:=9*x^2*(x^2+x+1)*diff(diff(y(x),x),x)+3*x*(13*x^2+7*x+1)*diff(y(x),x)+(25*x^2+4*x+1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.294 (sec). Leaf size: 58

ode=9*x^2*(1+x+x^2)*D[y[x],{x,2}]+3*x*(1+7*x+13*x^2)*D[y[x],x]+(1+4*x+25*x^2)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \sqrt {x} (c_2 \log (x)+c_1) \exp \left (-\frac {1}{2} \int _1^x\left (\frac {4 K[1]+2}{K[1]^2+K[1]+1}+\frac {1}{3 K[1]}\right )dK[1]\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*x**2*(x**2 + x + 1)*Derivative(y(x), (x, 2)) + 3*x*(13*x**2 + 7*x + 1)*Derivative(y(x), x) + (25*x**2 + 4*x + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False