74.3.14 problem 13 (c)

Internal problem ID [15874]
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 (c)
Date solved : Tuesday, January 28, 2025 at 08:11:12 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&={\frac {1}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.632 (sec). Leaf size: 31

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

\[ y = \frac {i \sqrt {3}\, {\mathrm e}^{t}}{4}+\frac {{\mathrm e}^{t}}{4}-\frac {i \sqrt {3}\, {\mathrm e}^{-t}}{4}+\frac {{\mathrm e}^{-t}}{4} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 32

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

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