59.1.251 problem 254

Internal problem ID [9423]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 254
Date solved : Wednesday, March 05, 2025 at 07:49:02 AM
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: 0.005 (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);
 

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

✓ Mathematica. Time used: 0.218 (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]
 

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

✗ 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