Internal problem ID [7578]
Book: Collection of Kovacic problems
Section: section 3. Problems from Kovacic related papers
Problem number: David Saunders 1981 paper. Example 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-2 y=0} \end {gather*}
✓ 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)
\[ y \relax (x ) = c_{1} x^{2}+\frac {c_{2}}{x} \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 18
DSolve[x^2*y''[x]== 2*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 x^3+c_1}{x} \\ \end{align*}