Internal problem ID [6942]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 211.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Laguerre]
Solve \begin {gather*} \boxed {t y^{\prime \prime }-\left (4+t \right ) y^{\prime }+2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 27
dsolve(t*diff(y(t),t$2)-(4+t)*diff(y(t),t)+2*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} \left (t^{2}+6 t +12\right )+c_{2} {\mathrm e}^{t} \left (t^{2}-6 t +12\right ) \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 63
DSolve[t*y''[t]-(4+t)*y'[t]+2*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {\sqrt {t} \left ((c_2-i c_1) (t (t+6)+12)+(i c_1+c_2) e^t ((t-6) t+12)\right )}{\sqrt {\pi } \sqrt {-i t}} \\ \end{align*}