59.1.435 problem 448

Internal problem ID [9607]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 448
Date solved : Sunday, March 30, 2025 at 02:38:33 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 19

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

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + 2*x*(x - 1)*Derivative(y(x), x) + (x**2 - 2*x + 2)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False