53.1.461 problem 476

Internal problem ID [10933]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 476
Date solved : Tuesday, September 30, 2025 at 07:33:12 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-2 x \left (x +2\right ) y^{\prime }+\left (x^{2}+4 x +6\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

ode:=x^2*diff(diff(y(x),x),x)-2*x*(x+2)*diff(y(x),x)+(x^2+4*x+6)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} x^{2} \left (c_2 x +c_1 \right ) \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 21

ode=x^2*D[y[x],{x,2}]-2*x*(x+2)*D[y[x],x]+(x^2+4*x+6)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{x+2} x^2 (c_2 x+c_1) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 2*x*(x + 2)*Derivative(y(x), x) + (x**2 + 4*x + 6)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False