Internal problem ID [7151]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 427.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Laguerre]
Solve \begin {gather*} \boxed {t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(t*diff(y(t),t$2)-(1+t)*diff(y(t),t)+y(t) = 0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} \left (t +1\right )+{\mathrm e}^{t} c_{2} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 19
DSolve[t*y''[t]-(1+t)*y'[t]+y[t] == 0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to c_1 e^t-c_2 (t+1) \\ \end{align*}