Internal problem ID [7838]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 353.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {4 \left (t^{2}-3 t +2\right ) y^{\prime \prime }-2 y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 62
dsolve(4*(t^2-3*t+2)*diff(y(t),t$2)-2*diff(y(t),t)+y(t)=0,y(t), singsol=all)
\[ y \left (t \right ) = c_{1} \sqrt {t -1}+\frac {c_{2} \sqrt {t -2}\, \left (t -1\right ) \left (\ln \left (t -\frac {3}{2}+\sqrt {t^{2}-3 t +2}\right ) \sqrt {t^{2}-3 t +2}-2 t +4\right )}{t^{2}-3 t +2} \]
✓ Solution by Mathematica
Time used: 0.257 (sec). Leaf size: 53
DSolve[4*(t^2-3*t+2)*y''[t]-2*y'[t]+y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \sqrt {1-t} \left (-2 c_2 \text {arctanh}\left (\frac {1}{\sqrt {\frac {t-1}{t-2}}}\right )+\frac {2 c_2}{\sqrt {\frac {t-1}{t-2}}}+c_1\right ) \]