Internal problem ID [8921]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1342.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {a y}{x^{4}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 31
dsolve(diff(diff(y(x),x),x) = -a/x^4*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} x \sinh \left (\frac {\sqrt {-a}}{x}\right )+c_{2} x \cosh \left (\frac {\sqrt {-a}}{x}\right ) \]
✓ Solution by Mathematica
Time used: 0.064 (sec). Leaf size: 52
DSolve[y''[x] == -((a*y[x])/x^4),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x e^{\frac {i \sqrt {a}}{x}}-\frac {i c_2 x e^{-\frac {i \sqrt {a}}{x}}}{2 \sqrt {a}} \\ \end{align*}