Internal problem ID [6935]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 204.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Laguerre]
Solve \begin {gather*} \boxed {2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 17
dsolve(2*t*diff(y(t),t$2)+(1-2*t)*diff(y(t),t)-y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} {\mathrm e}^{t} \erf \left (\sqrt {t}\right )+{\mathrm e}^{t} c_{2} \]
✓ Solution by Mathematica
Time used: 0.083 (sec). Leaf size: 21
DSolve[2*t*y''[t]+(1-2*t)*y'[t]-y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^t \left (c_1-c_2 \text {Gamma}\left (\frac {1}{2},t\right )\right ) \\ \end{align*}