Internal problem ID [7012]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 281.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+n^{2} y-\frac {6 y}{x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 61
dsolve(diff(y(x),x$2)+n^2*y(x)=6*y(x)/x^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (\left (n^{2} x^{2}-3\right ) \cos \left (n x \right )-3 \sin \left (n x \right ) n x \right )}{x^{2}}+\frac {c_{2} \left (3 \cos \left (n x \right ) n x +\left (n^{2} x^{2}-3\right ) \sin \left (n x \right )\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 77
DSolve[y''[x]+n^2*y[x]==6*y[x]/x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {\frac {2}{\pi }} \sqrt {x} \left (\left (c_1 \left (n^2 x^2-3\right )+3 c_2 n x\right ) \sin (n x)+(n x (3 c_1-c_2 n x)+3 c_2) \cos (n x)\right )}{(n x)^{5/2}} \\ \end{align*}