Internal problem ID [6932]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 200.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {t^{2} y^{\prime \prime }+y^{\prime } t +\left (t^{2}-\frac {1}{4}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.148 (sec). Leaf size: 19
dsolve(t^2*diff(y(t),t$2)+t*diff(y(t),t)+(t^2-1/4)*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = \frac {c_{1} \sin \relax (t )}{\sqrt {t}}+\frac {c_{2} \cos \relax (t )}{\sqrt {t}} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 39
DSolve[t^2*y''[t]+t*y'[t]+(t^2-1/4)*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {e^{-i t} \left (2 c_1-i c_2 e^{2 i t}\right )}{2 \sqrt {t}} \\ \end{align*}