59.3.9 problem David Saunders 1981 paper. Example 3

Internal problem ID [10011]
Book : Collection of Kovacic problems
Section : section 3. Problems from Kovacic related papers
Problem number : David Saunders 1981 paper. Example 3
Date solved : Monday, January 27, 2025 at 06:18:14 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Solution by Maple

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

dsolve(x^2*diff(y(x),x$2)= 2*y(x),y(x), singsol=all)
 

\[ y = \frac {c_{2} x^{3}+c_{1}}{x} \]

✓ Solution by Mathematica

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

DSolve[x^2*D[y[x],{x,2}]== 2*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 x^3+c_1}{x} \]