59.2.4 problem 4

Internal problem ID [9997]
Book : Collection of Kovacic problems
Section : section 2. Solution found using all possible Kovacic cases
Problem number : 4
Date solved : Monday, January 27, 2025 at 06:16:34 PM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 27

dsolve(diff(y(x),x$2)-1/(4*x^2)*y(x)=0,y(x), singsol=all)
 

\[ y = \sqrt {x}\, \left (x^{\frac {\sqrt {2}}{2}} c_{1} +x^{-\frac {\sqrt {2}}{2}} c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 32

DSolve[D[y[x],{x,2}]-1/(4*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^{\frac {1}{2}-\frac {1}{\sqrt {2}}} \left (c_2 x^{\sqrt {2}}+c_1\right ) \]