Internal problem ID [7083]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 354.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.093 (sec). Leaf size: 32
dsolve(2*(t^2-5*t+6)*diff(y(t),t$2)+(2*t-3)*diff(y(t),t)-8*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} \left (t^{2}-\frac {13}{3} t +\frac {37}{8}\right )+\frac {c_{2} \left (6 t -17\right ) \left (t -2\right )^{\frac {3}{2}}}{\sqrt {t -3}} \]
✓ Solution by Mathematica
Time used: 0.18 (sec). Leaf size: 78
DSolve[2*(t^2-5*t+6)*y''[t]+(2*t-3)*y'[t]-8*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {\sqrt [4]{2-t} \sqrt [4]{\frac {t-3}{t-2}} \left (5 c_1 (6 t-17) (t-2)^{3/2}+24 c_2 \sqrt {t-3} (8 t (3 t-13)+111)\right )}{30 (3-t)^{3/4}} \\ \end{align*}