Internal problem ID [8929]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1350.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 21
dsolve(diff(diff(y(x),x),x) = -2/x*diff(y(x),x)-a^2/x^4*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sin \left (\frac {a}{x}\right )+c_{2} \cos \left (\frac {a}{x}\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 25
DSolve[y''[x] == -((a^2*y[x])/x^4) - (2*y'[x])/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cos \left (\frac {a}{x}\right )-c_2 \sin \left (\frac {a}{x}\right ) \\ \end{align*}