Internal problem ID [7514]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 797.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.089 (sec). Leaf size: 48
dsolve(4*(t^2-3*t+2)*diff(y(t),t$2)-2*diff(y(t),t)+y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} \sqrt {t -1}+\frac {c_{2} \left (-\frac {\sqrt {t^{2}-3 t +2}\, \ln \left (-\frac {3}{2}+t +\sqrt {t^{2}-3 t +2}\right )}{2}+t -2\right )}{\sqrt {t -2}} \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 49
DSolve[4*(t^2-3*t+2)*y''[t]-2*y'[t]+y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \sqrt {1-t} \left (\frac {2 c_2}{\sqrt {\frac {1}{t-2}+1}}-2 c_2 \coth ^{-1}\left (\sqrt {\frac {1}{t-2}+1}\right )+c_1\right ) \\ \end{align*}