Internal problem ID [8122]
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: 48
dsolve(t*diff(y(t),t$2)+t*diff(y(t),t)+2*y(t)=0,y(t), singsol=all)
\[ y \left (t \right ) = c_{1} {\mathrm e}^{-t} \left (t -2\right ) t +\frac {c_{2} \left (\operatorname {expIntegral}_{1}\left (-t \right ) t^{2}+{\mathrm e}^{t} t -2 \,\operatorname {expIntegral}_{1}\left (-t \right ) t -{\mathrm e}^{t}\right ) {\mathrm e}^{-t}}{2} \]
✓ Solution by Mathematica
Time used: 0.07 (sec). Leaf size: 51
DSolve[t*y''[t]+t*y'[t]+2*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} e^{-t} \left (c_2 (t-2) t \operatorname {ExpIntegralEi}(t)+2 c_1 t^2-t \left (c_2 e^t+4 c_1\right )+c_2 e^t\right ) \]