79.1.10 problem 2 (iv)

Internal problem ID [18497]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 3. Solutions of first-order equations. Exercises at page 47
Problem number : 2 (iv)
Date solved : Tuesday, January 28, 2025 at 11:50:58 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} x \left (0\right )&=1 \end{align*}

✓ Solution by Maple

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

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

\[ x = 1 \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 18

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

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