59.1.333 problem 340

Internal problem ID [9505]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 340
Date solved : Sunday, March 30, 2025 at 02:36:24 PM
CAS classification : [_Laguerre]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

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

\[ y = c_1 \,{\mathrm e}^{x}+c_2 \left (x^{2}+2 x +2\right ) \]

✓ Mathematica. Time used: 0.216 (sec). Leaf size: 35

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

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

✗ Sympy

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

False