Internal problem ID [7696]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 209.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Lienard]
\[ \boxed {t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+y t=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 47
dsolve(t*diff(y(t),t$2)-(t^2+2)*diff(y(t),t)+t*y(t)=0,y(t), singsol=all)
\[ y \left (t \right ) = c_{1} {\mathrm e}^{\frac {t^{2}}{2}}+\frac {c_{2} {\mathrm e}^{\frac {t^{2}}{2}} \left (-\sqrt {\pi }\, \sqrt {2}\, \operatorname {erf}\left (\frac {\sqrt {2}\, t}{2}\right )+2 t \,{\mathrm e}^{-\frac {t^{2}}{2}}\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.13 (sec). Leaf size: 52
DSolve[t*y''[t]-(t^2+2)*y'[t]+t*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \sqrt {\frac {\pi }{2}} c_2 e^{\frac {t^2}{2}} \text {erf}\left (\frac {t}{\sqrt {2}}\right )+c_1 e^{\frac {t^2}{2}}-c_2 t \]