74.3.12 problem 13 (a)

Internal problem ID [15793]
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 (a)
Date solved : Thursday, March 13, 2025 at 06:20:20 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Maple. Time used: 1.349 (sec). Leaf size: 27

ode:=diff(y(t),t) = (-1+y(t)^2)^(1/2); 
ic:=y(0) = 2; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \frac {{\mathrm e}^{t} \sqrt {3}}{2}+{\mathrm e}^{t}-\frac {\sqrt {3}\, {\mathrm e}^{-t}}{2}+{\mathrm e}^{-t} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 36

ode=D[y[t],t]==Sqrt[y[t]^2-1]; 
ic={y[0]==2}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {1}{2} e^{-t} \left (\left (2+\sqrt {3}\right ) e^{2 t}+2-\sqrt {3}\right ) \]

✗ Sympy

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

NotImplementedError : Initial conditions produced too many solutions for constants