59.3.2 problem Kovacic 1985 paper. page 14. section 3.2, example 2

Internal problem ID [10004]
Book : Collection of Kovacic problems
Section : section 3. Problems from Kovacic related papers
Problem number : Kovacic 1985 paper. page 14. section 3.2, example 2
Date solved : Monday, January 27, 2025 at 06:16:39 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=\left (\frac {6}{x^{2}}-1\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 41

dsolve(diff(y(x),x$2)= ( (4*(5/2)^2-1)/(4*x^2)-1)*y(x),y(x), singsol=all)
 

\[ y = \frac {\left (c_{1} x^{2}+3 c_{2} x -3 c_{1} \right ) \cos \left (x \right )+\sin \left (x \right ) \left (c_{2} x^{2}-3 c_{1} x -3 c_{2} \right )}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 21

DSolve[D[y[x],{x,2}]== ( (4*(5/2)^2-1)/(4*x^2)-1)*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x (c_1 j_2(x)-c_2 y_2(x)) \]