53.1.711 problem 728

Internal problem ID [11183]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 728
Date solved : Tuesday, September 30, 2025 at 07:36:43 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }-2 \left (x +1\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*(1+x)*diff(y(x),x)+(x+2)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} \left (c_2 \,x^{3}+c_1 \right ) \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to \frac {1}{3} e^{x+1} \left (c_2 x^3+3 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)*y(x) - (2*x + 2)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False