53.1.260 problem 263

Internal problem ID [10732]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 263
Date solved : Tuesday, September 30, 2025 at 07:31:27 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 24

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

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

✓ Mathematica. Time used: 0.12 (sec). Leaf size: 33

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

\begin{align*} y(x)&\to \frac {c_2 \int _1^xe^{-K[1]} K[1]^2dK[1]+c_1}{x} \end{align*}

✗ Sympy

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

False