Internal problem ID [7566]
Book: Collection of Kovacic problems
Section: section 2. Solution found using all possible Kovacic cases
Problem number: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {y}{x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x$2)+1/x^2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sqrt {x}\, \sin \left (\frac {\sqrt {3}\, \ln \relax (x )}{2}\right )+c_{2} \sqrt {x}\, \cos \left (\frac {\sqrt {3}\, \ln \relax (x )}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 42
DSolve[y''[x]+1/x^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {x} \left (c_1 \cos \left (\frac {1}{2} \sqrt {3} \log (x)\right )+c_2 \sin \left (\frac {1}{2} \sqrt {3} \log (x)\right )\right ) \\ \end{align*}