Internal problem ID [13817]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-\sqrt {y^{2}-1}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.156 (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: 0.067 (sec). Leaf size: 49
DSolve[{y'[t]==Sqrt[y[t]^2-1],{y[0]==2}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} e^{-t} \sqrt {2 e^{2 t}+\left (7+4 \sqrt {3}\right ) e^{4 t}+7-4 \sqrt {3}} \]