Internal problem ID [6341]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 51.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {t^{2} y^{\prime \prime }-2 y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(t^2*diff(y(t),t$2)-2*diff(y(t),t)=0,y(t), singsol=all)
\[ y \left (t \right ) = c_{1} +\left (t \,{\mathrm e}^{-\frac {2}{t}}-2 \,\operatorname {Ei}_{1}\left (\frac {2}{t}\right )\right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 29
DSolve[t^2*y''[t]-2*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 2 c_1 \operatorname {ExpIntegralEi}\left (-\frac {2}{t}\right )+c_1 e^{-2/t} t+c_2 \\ \end{align*}