59.1.237 problem 240

Internal problem ID [9409]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 240
Date solved : Sunday, March 30, 2025 at 02:34:19 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+\left (4-x \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 21

ode:=x^2*diff(diff(y(x),x),x)+x*(x-3)*diff(y(x),x)+(-x+4)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.396 (sec). Leaf size: 60

ode=x^2*D[y[x],{x,2}]+x*(x-3)*D[y[x],x]+(4-x)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \sqrt {x} \left (c_2 \int _1^x\frac {e^{K[2]}}{K[2]}dK[2]+c_1\right ) \exp \left (\frac {1}{2} \left (-\int _1^x\left (1-\frac {3}{K[1]}\right )dK[1]-x\right )\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + x*(x - 3)*Derivative(y(x), x) + (4 - x)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False