59.3.4 problem Kovacic 1985 paper. page 19. section 4.2. Example 1

Internal problem ID [10006]
Book : Collection of Kovacic problems
Section : section 3. Problems from Kovacic related papers
Problem number : Kovacic 1985 paper. page 19. section 4.2. Example 1
Date solved : Monday, January 27, 2025 at 06:16:41 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=\left (\frac {1}{x}-\frac {3}{16 x^{2}}\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 25

dsolve(diff(y(x),x$2)= (1/x-3/(16*x^2))*y(x),y(x), singsol=all)
 

\[ y = x^{{1}/{4}} \left (c_{1} \sinh \left (2 \sqrt {x}\right )+c_{2} \cosh \left (2 \sqrt {x}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.055 (sec). Leaf size: 41

DSolve[D[y[x],{x,2}]== (1/x-3/(16*x^2))*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{-2 \sqrt {x}} \sqrt [4]{x} \left (2 c_1 e^{4 \sqrt {x}}-c_2\right ) \]