Internal problem ID [7361]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 642.
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}+t \right ) y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 20
dsolve(t^2*diff(y(t),t$2)+(t-t^2)*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: 0.01 (sec). Leaf size: 23
DSolve[t^2*y''[t]+(t-t^2)*y'[t]-y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {c_2 e^t-c_1 (t+1)}{t} \\ \end{align*}