59.3.7 problem Kovacic 2005 paper. Example 2

Internal problem ID [10009]
Book : Collection of Kovacic problems
Section : section 3. Problems from Kovacic related papers
Problem number : Kovacic 2005 paper. Example 2
Date solved : Wednesday, March 05, 2025 at 08:04:09 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 14

ode:=diff(diff(y(x),x),x) = -1/4/x^2*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_{2} \ln \left (x \right )+c_{1} \right ) \sqrt {x} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 24

ode=D[y[x],{x,2}]== -1/(4*x^2)*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{2} \sqrt {x} (c_2 \log (x)+2 c_1) \]

✓ Sympy. Time used: 0.062 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = \sqrt {x} \left (C_{1} + C_{2} \log {\left (x \right )}\right ) \]