Internal problem ID [7564]
Book: Collection of Kovacic problems
Section: section 2. Solution found using all possible Kovacic cases
Problem number: 4.
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: 0.002 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)-1/(4*x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{\frac {\sqrt {2}}{2}+\frac {1}{2}}+c_{2} x^{-\frac {\sqrt {2}}{2}+\frac {1}{2}} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 32
DSolve[y''[x]-1/(4*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^{\frac {1}{2}-\frac {1}{\sqrt {2}}} \left (c_2 x^{\sqrt {2}}+c_1\right ) \\ \end{align*}