Internal problem ID [7365]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 647.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {t y^{\prime \prime }+t y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(t*diff(y(t),t$2)+t*diff(y(t),t)+2*y(t)=0,y(t), singsol=all)
\[ y \left (t \right ) = c_{1} {\mathrm e}^{-t} \left (t -2\right ) t +c_{2} \left ({\mathrm e}^{-t} \left (t -2\right ) t \,\operatorname {Ei}_{1}\left (-t \right )+t -1\right ) \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 37
DSolve[t*y''[t]+t*y'[t]+2*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{2} \left (e^{-t} (t-2) t (c_2 \operatorname {ExpIntegralEi}(t)+2 c_1)-c_2 (t-1)\right ) \\ \end{align*}