Internal problem ID [7099]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 370.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {y}{2 x^{4}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)+1/(2*x^4)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x \sin \left (\frac {\sqrt {2}}{2 x}\right )+c_{2} x \cos \left (\frac {\sqrt {2}}{2 x}\right ) \]
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 50
DSolve[y''[x]+1/(2*x^4)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{\frac {i}{\sqrt {2} x}} x-\frac {i c_2 e^{-\frac {i}{\sqrt {2} x}} x}{\sqrt {2}} \\ \end{align*}