Internal problem ID [6937]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 206.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 t^{2} y^{\prime \prime }-y^{\prime } t +\left (t +1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve(2*t^2*diff(y(t),t$2)-t*diff(y(t),t)+(1+t)*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} \sin \left (\sqrt {2}\, \sqrt {t}\right ) \sqrt {t}+c_{2} \sqrt {t}\, \cos \left (\sqrt {2}\, \sqrt {t}\right ) \]
✓ Solution by Mathematica
Time used: 0.062 (sec). Leaf size: 62
DSolve[2*t^2*y''[t]-t*y'[t]+(1+t)*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{2} e^{-i \sqrt {2} \sqrt {t}} \sqrt {t} \left (2 c_1 e^{2 i \sqrt {2} \sqrt {t}}+i \sqrt {2} c_2\right ) \\ \end{align*}