17.5.4 problem 1.1-6 (d)

Internal problem ID [3437]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.1-6, page 7
Problem number : 1.1-6 (d)
Date solved : Tuesday, March 04, 2025 at 04:39:05 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=1-y^{2} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 8

ode:=diff(y(t),t) = 1-y(t)^2; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \tanh \left (t +c_{1} \right ) \]

✓ Mathematica. Time used: 0.634 (sec). Leaf size: 44

ode=D[y[t],t]==1-y[t]^2; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)\to \frac {e^{2 t}-e^{2 c_1}}{e^{2 t}+e^{2 c_1}} \\ y(t)\to -1 \\ y(t)\to 1 \\ \end{align*}

✓ Sympy. Time used: 0.816 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t)**2 + Derivative(y(t), t) - 1,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = - \frac {1}{\tanh {\left (C_{1} - t \right )}} \]