53.1.653 problem 670

Internal problem ID [11125]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 670
Date solved : Tuesday, September 30, 2025 at 07:36:08 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x y^{\prime \prime }-x y^{\prime }+2 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 33

ode:=4*x*diff(diff(y(x),x),x)-x*diff(y(x),x)+2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2 x \left (x -8\right ) \operatorname {Ei}_{1}\left (-\frac {x}{4}\right )}{16}+\frac {c_2 \left (x -4\right ) {\mathrm e}^{\frac {x}{4}}}{4}+c_1 x \left (x -8\right ) \]

✓ Mathematica. Time used: 0.121 (sec). Leaf size: 42

ode=4*x*D[y[x],{x,2}]-x*D[y[x],x]+2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to (x-8) x \left (c_2 \int _1^x\frac {e^{\frac {K[1]}{4}}}{(K[1]-8)^2 K[1]^2}dK[1]+c_1\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*Derivative(y(x), x) + 4*x*Derivative(y(x), (x, 2)) + 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False