Internal problem ID [8121]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 646.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve(t^2*diff(y(t),t$2)+(t^2-3*t)*diff(y(t),t)+3*y(t)=0,y(t), singsol=all)
\[ y \left (t \right ) = c_{1} t^{3} {\mathrm e}^{-t}+\frac {c_{2} t \,{\mathrm e}^{-t} \left (\operatorname {expIntegral}_{1}\left (-t \right ) t^{2}+{\mathrm e}^{t} t +{\mathrm e}^{t}\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 41
DSolve[t^2*y''[t]+(t^2-3*t)*y'[t]+3*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} e^{-t} \left (c_1 t^3 \operatorname {ExpIntegralEi}(t)+2 c_2 t^3-c_1 e^t (t+1) t\right ) \]