63.1.28 problem 45

Internal problem ID [15468]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 45
Date solved : Thursday, October 02, 2025 at 10:15:39 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

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

\[ s = \left (-\ln \left (t \right )+c_1 \right ) t \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 14

ode=(t-s[t])+t*D[s[t],t]==0; 
ic={}; 
DSolve[{ode,ic},s[t],t,IncludeSingularSolutions->True]
 

\begin{align*} s(t)&\to t (-\log (t)+c_1) \end{align*}

✓ Sympy. Time used: 0.093 (sec). Leaf size: 8

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

\[ s{\left (t \right )} = t \left (C_{1} - \log {\left (t \right )}\right ) \]