Internal problem ID [7573]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\left (\frac {1}{x}-\frac {3}{16 x^{2}}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)= (1/x-3/(16*x^2))*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{\frac {1}{4}} \sinh \left (2 \sqrt {x}\right )+c_{2} x^{\frac {1}{4}} \cosh \left (2 \sqrt {x}\right ) \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 41
DSolve[y''[x]== (1/x-3/(16*x^2))*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{-2 \sqrt {x}} \sqrt [4]{x} \left (2 c_1 e^{4 \sqrt {x}}-c_2\right ) \\ \end{align*}