59.1.643 problem 660

Internal problem ID [9815]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 660
Date solved : Sunday, March 30, 2025 at 02:47:14 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.199 (sec). Leaf size: 33

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

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

✗ Sympy

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

False