Internal problem ID [7698]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 211.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Laguerre]
\[ \boxed {t y^{\prime \prime }-\left (t +4\right ) y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (t \right ) = c_{1} \left (t^{2}+6 t +12\right )+c_{2} {\mathrm e}^{t} \left (t^{2}-6 t +12\right ) \]
✓ Solution by Mathematica
Time used: 0.064 (sec). Leaf size: 85
DSolve[t*y''[t]-(4+t)*y'[t]+2*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {2 e^{t/2} \sqrt {t} \left (\left (c_2 t^2-6 i c_1 t+12 c_2\right ) \cosh \left (\frac {t}{2}\right )+i \left (c_1 \left (t^2+12\right )+6 i c_2 t\right ) \sinh \left (\frac {t}{2}\right )\right )}{\sqrt {\pi } \sqrt {-i t}} \]