59.1.819 problem 843

Internal problem ID [9991]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 843
Date solved : Monday, January 27, 2025 at 06:16:30 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} y^{\prime \prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 9

dsolve(diff(y(x),x$2)=((4*(1/2)^2-1)/(4*x^2))*y(x),y(x), singsol=all)
 

\[ y = c_{1} x +c_{2} \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 12

DSolve[D[y[x],{x,2}]==((4*(1/2)^2-1)/(4*x^2))*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 x+c_1 \]