59.1.441 problem 454

Internal problem ID [9613]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 454
Date solved : Sunday, March 30, 2025 at 02:38:40 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 19

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

\[ y(x)\to \frac {e^x (c_2 x+c_1)}{x} \]

✗ Sympy

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

False