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 : Monday, January 27, 2025 at 07:36:42 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[D[y[t],t]==1-y[t]^2,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*}