Internal problem ID [6747]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 13.
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 +2\right ) y^{\prime }+\left (t +2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 13
dsolve(t^2*diff(y(t),t$2)-t*(t+2)*diff(y(t),t)+(t+2)*y(t) = 0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} t +c_{2} {\mathrm e}^{t} t \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 16
DSolve[t^2*y''[t]-t*(t+2)*y'[t]+(t+2)*y[t] == 0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to t \left (c_2 e^t+c_1\right ) \\ \end{align*}