59.1.278 problem 281

Internal problem ID [9450]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 281
Date solved : Monday, January 27, 2025 at 06:02:57 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+n^{2} y&=\frac {6 y}{x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 53

dsolve(diff(y(x),x$2)+n^2*y(x)=6*y(x)/x^2,y(x), singsol=all)
 

\[ y = \frac {\left (c_{1} n^{2} x^{2}+3 c_{2} n x -3 c_{1} \right ) \cos \left (n x \right )+\sin \left (n x \right ) \left (c_{2} n^{2} x^{2}-3 c_{1} n x -3 c_{2} \right )}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.123 (sec). Leaf size: 79

DSolve[D[y[x],{x,2}]+n^2*y[x]==6*y[x]/x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {\sqrt {\frac {2}{\pi }} \sqrt {x} \left (\left (c_2 \left (-n^2\right ) x^2+3 c_1 n x+3 c_2\right ) \cos (n x)+\left (c_1 \left (n^2 x^2-3\right )+3 c_2 n x\right ) \sin (n x)\right )}{(n x)^{5/2}} \]