58.2.16 problem 17

Internal problem ID [9139]
Book : Second order enumerated odes
Section : section 2
Problem number : 17
Date solved : Monday, January 27, 2025 at 05:48:45 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (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)
 

\[ y = c_{1} \sin \left (\frac {a}{x}\right )+c_{2} \cos \left (\frac {a}{x}\right ) \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 25

DSolve[D[y[x],{x,2}]+2/x*D[y[x],x]+a^2/x^4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \cos \left (\frac {a}{x}\right )-c_2 \sin \left (\frac {a}{x}\right ) \]