59.1.757 problem 779

Internal problem ID [9929]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 779
Date solved : Monday, January 27, 2025 at 06:15:52 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 27

dsolve(x^2*diff(y(x),x$2)+(x^2-2)*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 21

DSolve[x^2*D[y[x],{x,2}]+(x^2-2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x (c_1 j_1(x)-c_2 y_1(x)) \]