Internal problem ID [7576]
Book: Collection of Kovacic problems
Section: section 3. Problems from Kovacic related papers
Problem number: Kovacic 2005 paper. Example 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {y}{4 x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 17
dsolve(diff(y(x),x$2)= -1/(4*x^2)*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sqrt {x}+c_{2} \sqrt {x}\, \ln \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 24
DSolve[y''[x]== -1/(4*x^2)*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \sqrt {x} (c_2 \log (x)+2 c_1) \\ \end{align*}