Internal problem ID [7503]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve(t^2*diff(y(t),t$2)-t*(t+2)*diff(y(t),t)+(t+2)*y(t) = 0,y(t), singsol=all)
\[ y \left (t \right ) = c_{1} t +c_{2} t \,{\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 16
DSolve[t^2*y''[t]-t*(t+2)*y'[t]+(t+2)*y[t] == 0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to t \left (c_2 e^t+c_1\right ) \]