Internal problem ID [6938]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 207.
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 }+\left (t^{2}-t \right ) y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.086 (sec). Leaf size: 29
dsolve(2*t^2*diff(y(t),t$2)+(t^2-t)*diff(y(t),t)+y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} \WhittakerM \left (\frac {1}{4}, \frac {1}{4}, \frac {t}{2}\right ) t^{\frac {1}{4}} {\mathrm e}^{-\frac {t}{4}}+c_{2} \sqrt {t}\, {\mathrm e}^{-\frac {t}{2}} \]
✓ Solution by Mathematica
Time used: 0.05 (sec). Leaf size: 36
DSolve[2*t^2*y''[t]+(t^2-t)*y'[t]+y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-t/2} \left (c_2 \sqrt {t}-c_1 t E_{\frac {1}{2}}\left (-\frac {t}{2}\right )\right ) \\ \end{align*}