56.1.51 problem 51

Internal problem ID [8763]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 51
Date solved : Monday, January 27, 2025 at 04:48:29 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} t^{2} y^{\prime \prime }-2 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 25

dsolve(t^2*diff(y(t),t$2)-2*diff(y(t),t)=0,y(t), singsol=all)
 

\[ y = {\mathrm e}^{-\frac {2}{t}} c_{2} t -2 \,\operatorname {Ei}_{1}\left (\frac {2}{t}\right ) c_{2} +c_{1} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 29

DSolve[t^2*D[y[t],{t,2}]-2*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 2 c_1 \operatorname {ExpIntegralEi}\left (-\frac {2}{t}\right )+c_1 e^{-2/t} t+c_2 \]