85.33.57 problem 57

Internal problem ID [22680]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 65
Problem number : 57
Date solved : Thursday, October 02, 2025 at 09:06:19 PM
CAS classification : [[_homogeneous, `class C`], [_Abel, `2nd type`, `class C`], _dAlembert]

\begin{align*} s^{\prime }&=\frac {1}{s+t +1} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 21

ode:=diff(s(t),t) = 1/(s(t)+t+1); 
dsolve(ode,s(t), singsol=all);
 

\[ s = -\operatorname {LambertW}\left (-c_1 \,{\mathrm e}^{-t -2}\right )-t -2 \]

✓ Mathematica. Time used: 60.031 (sec). Leaf size: 24

ode=D[s[t],t]==1/(s[t]+t+1); 
ic={}; 
DSolve[{ode,ic},s[t],t,IncludeSingularSolutions->True]
 

\begin{align*} s(t)&\to -W\left (c_1 \left (-e^{-t-2}\right )\right )-t-2 \end{align*}

✓ Sympy. Time used: 0.378 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
s = Function("s") 
ode = Eq(Derivative(s(t), t) - 1/(t + s(t) + 1),0) 
ics = {} 
dsolve(ode,func=s(t),ics=ics)
 

\[ s{\left (t \right )} = - t - W\left (C_{1} e^{- t - 2}\right ) - 2 \]