Internal problem ID [8124]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 649.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve(t^2*diff(y(t),t$2)-t*(1+t)*diff(y(t),t)+y(t)=0,y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{t} c_{1} t +c_{2} {\mathrm e}^{t} t \,\operatorname {Ei}_{1}\left (t \right ) \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 20
DSolve[t^2*y''[t]-t*(1+t)*y'[t]+y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^t t (c_1 \operatorname {ExpIntegralEi}(-t)+c_2) \]