59.1.118 problem 120

Internal problem ID [9290]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 120
Date solved : Sunday, March 30, 2025 at 02:31:36 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.017 (sec). Leaf size: 23

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

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

✓ Mathematica. Time used: 0.182 (sec). Leaf size: 52

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

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

✗ Sympy

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

False