59.2.2 problem 2

Internal problem ID [9995]
Book : Collection of Kovacic problems
Section : section 2. Solution found using all possible Kovacic cases
Problem number : 2
Date solved : Monday, January 27, 2025 at 06:16:33 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} y^{\prime \prime }&=\frac {20 y}{x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(diff(y(x),x$2)=((4*(9/2)^2-1)/(4*x^2))*y(x),y(x), singsol=all)
 

\[ y = \frac {c_{1} x^{9}+c_{2}}{x^{4}} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 18

DSolve[D[y[x],{x,2}]==((4*(9/2)^2-1)/(4*x^2))*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 x^9+c_1}{x^4} \]