68.3.15 problem 13 (d)

Internal problem ID [17162]
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 (d)
Date solved : Thursday, October 02, 2025 at 01:45:42 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (2\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 5

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

\[ y = 1 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 6

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

\begin{align*} y(t)&\to 1 \end{align*}

✓ Sympy. Time used: 0.464 (sec). Leaf size: 7

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

\[ y{\left (t \right )} = \cosh {\left (t - 2 \right )} \]