50.1.50 problem 50

Internal problem ID [10048]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 50
Date solved : Tuesday, September 30, 2025 at 06:51:01 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 10

ode:=t*diff(diff(y(t),t),t)+diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_2 \ln \left (t \right )+c_1 \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 13

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

\begin{align*} y(t)&\to c_1 \log (t)+c_2 \end{align*}

✓ Sympy. Time used: 0.062 (sec). Leaf size: 8

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

\[ y{\left (t \right )} = C_{1} + C_{2} \log {\left (t \right )} \]