59.1.248 problem 251

Internal problem ID [9420]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 251
Date solved : Wednesday, March 05, 2025 at 07:48:59 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 28

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

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

✓ Mathematica. Time used: 0.239 (sec). Leaf size: 33

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

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

✗ 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) + (2*x + 2)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False