74.3.12 problem 13 (a)

Internal problem ID [15872]
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 : Tuesday, January 28, 2025 at 08:10:54 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*}

✓ Solution by Maple

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

dsolve([diff(y(t),t)=sqrt(y(t)^2-1),y(0) = 2],y(t), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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