Internal problem ID [7691]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 204.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Laguerre]
\[ \boxed {2 t y^{\prime \prime }+\left (1-2 t \right ) y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(2*t*diff(y(t),t$2)+(1-2*t)*diff(y(t),t)-y(t)=0,y(t), singsol=all)
\[ y \left (t \right ) = c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{t} \left (\int \frac {{\mathrm e}^{-t}}{\sqrt {t}}d t \right ) \]
✓ Solution by Mathematica
Time used: 0.109 (sec). Leaf size: 21
DSolve[2*t*y''[t]+(1-2*t)*y'[t]-y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^t \left (c_1-c_2 \Gamma \left (\frac {1}{2},t\right )\right ) \]