53.1.676 problem 693

Internal problem ID [11148]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 693
Date solved : Tuesday, September 30, 2025 at 07:36:23 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 25

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

\[ y = \frac {-{\mathrm e}^{-x} c_2 +x \left (c_2 \,\operatorname {Ei}_{1}\left (x \right )+c_1 \right )}{x^{2}} \]

✓ Mathematica. Time used: 0.128 (sec). Leaf size: 36

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

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

✗ Sympy

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

False