Internal problem ID [7366]
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]]
Solve \begin {gather*} \boxed {t y^{\prime \prime }+y^{\prime } t +2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve(t*diff(y(t),t$2)+t*diff(y(t),t)+2*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} {\mathrm e}^{-t} t \left (t -2\right )+c_{2} \left ({\mathrm e}^{-t} t \left (t -2\right ) \expIntegral \left (1, -t \right )+t -1\right ) \]
✓ Solution by Mathematica
Time used: 0.06 (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 \text {Ei}(t)+2 c_1)-c_2 (t-1)\right ) \\ \end{align*}