56.1.51 problem 51

Internal problem ID [8763]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 51
Date solved : Wednesday, March 05, 2025 at 06:46:07 AM
CAS classification : [[_2nd_order, _missing_y]]

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

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

ode:=t^2*diff(diff(y(t),t),t)-2*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

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

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

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

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

✓ Sympy. Time used: 0.793 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t**2*Derivative(y(t), (t, 2)) - 2*Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} - C_{2} t e^{- \frac {2}{t}} - 2 C_{2} \operatorname {Ei}{\left (\frac {2 e^{i \pi }}{t} \right )} \]