Internal problem ID [6943]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 212.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 33
dsolve(t^2*diff(y(t),t$2)+(t^2-3*t)*diff(y(t),t)+3*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} t^{3} {\mathrm e}^{-t}+c_{2} t \left ({\mathrm e}^{-t} \expIntegral \left (1, -t \right ) t^{2}+t +1\right ) \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 37
DSolve[t^2*y''[t]+(t^2-3*t)*y'[t]+3*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{2} t \left (e^{-t} t^2 (c_1 \text {Ei}(t)+2 c_2)-c_1 (t+1)\right ) \\ \end{align*}