Internal problem ID [6946]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 215.
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 }-t \left (t +1\right ) y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 18
dsolve(t^2*diff(y(t),t$2)-t*(1+t)*diff(y(t),t)+y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} {\mathrm e}^{t} t +c_{2} {\mathrm e}^{t} t \expIntegral \left (1, t\right ) \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 20
DSolve[t^2*y''[t]-t*(1+t)*y'[t]+y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^t t (c_1 \operatorname {Ei}(-t)+c_2) \\ \end{align*}