Internal problem ID [7120]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 394.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-x y^{\prime }-\left (x^{2}+\frac {5}{4}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.144 (sec). Leaf size: 27
dsolve(x^2*diff(y(x),x$2)-x*diff(y(x),x)-(x^2+5/4)*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} {\mathrm e}^{x} \left (x -1\right )}{\sqrt {x}}+\frac {c_{2} {\mathrm e}^{-x} \left (x +1\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 53
DSolve[x^2*y''[x]-x*y'[x]-(x^2+5/4)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {\frac {2}{\pi }} ((i c_2 x+c_1) \sinh (x)-(c_1 x+i c_2) \cosh (x))}{\sqrt {-i x}} \\ \end{align*}