53.1.762 problem 784

Internal problem ID [11234]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 784
Date solved : Tuesday, September 30, 2025 at 07:37:10 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: 0.131 (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]
 

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

✗ 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