Internal problem ID [7358]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 639.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 56
dsolve(2*t*diff(y(t),t$2)+(1+t)*diff(y(t),t)-2*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} \left (\erf \left (\frac {\sqrt {2}\, \sqrt {t}}{2}\right ) \sqrt {\pi }\, \left (t^{2}+6 t +3\right )+\sqrt {2}\, \left (t^{\frac {3}{2}}+5 \sqrt {t}\right ) {\mathrm e}^{-\frac {t}{2}}\right )+c_{2} \left (t^{2}+6 t +3\right ) \]
✓ Solution by Mathematica
Time used: 0.158 (sec). Leaf size: 64
DSolve[2*t*y''[t]+(1+t)*y'[t]-2*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{24} \left ((t (t+6)+3) \left (\sqrt {2 \pi } c_2 \text {Erf}\left (\frac {\sqrt {t}}{\sqrt {2}}\right )+24 c_1\right )+2 c_2 e^{-t/2} \sqrt {t} (t+5)\right ) \\ \end{align*}