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 : Monday, January 27, 2025 at 06:18:13 PM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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