Internal problem ID [6941]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 210.
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: 22
dsolve(t^2*diff(y(t),t$2)+t*(t+1)*diff(y(t),t)-y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = \frac {c_{1} \left (t -1\right )}{t}+\frac {c_{2} {\mathrm e}^{-t}}{t} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 26
DSolve[t^2*y''[t]+t*(t+1)*y'[t]-y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {e^{-t} \left (c_1 e^t (t-1)+c_2\right )}{t} \\ \end{align*}