59.1.702 problem 719

Internal problem ID [9874]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 719
Date solved : Monday, January 27, 2025 at 06:15:17 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 48

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

\[ y = \frac {c_{2} \left (a^{2} x^{2}+3 a x +3\right ) {\mathrm e}^{-a x}+{\mathrm e}^{a x} c_{1} \left (a^{2} x^{2}-3 a x +3\right )}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.134 (sec). Leaf size: 90

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

\[ y(x)\to \frac {\sqrt {\frac {2}{\pi }} \left (\left (a^2 c_2 x^2-3 i a c_1 x+3 c_2\right ) \cosh (a x)+i \left (c_1 \left (a^2 x^2+3\right )+3 i a c_2 x\right ) \sinh (a x)\right )}{a^2 x^{3/2} \sqrt {-i a x}} \]