Internal problem ID [6701]
Book: Second order enumerated odes
Section: section 2
Problem number: 17.
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: 0.015 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)+2/x*diff(y(x),x)+a^2/x^4*y(x)=0,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: 0.007 (sec). Leaf size: 25
DSolve[y''[x]+2/x*y'[x]+a^2/x^4*y[x]==0,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*}