74.3.13 problem 13 (b)

Internal problem ID [15794]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number : 13 (b)
Date solved : Thursday, March 13, 2025 at 06:21:44 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (4\right )&=-1 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 5

ode:=diff(y(t),t) = (-1+y(t)^2)^(1/2); 
ic:=y(4) = -1; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = -1 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 6

ode=D[y[t],t]==Sqrt[y[t]^2-1]; 
ic={y[4]==-1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to -1 \]

✓ Sympy. Time used: 0.715 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-sqrt(y(t)**2 - 1) + Derivative(y(t), t),0) 
ics = {y(4): -1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = - \cosh {\left (t - 4 \right )} \]