Internal problem ID [14139]
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).
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*} \left [y \left (0\right ) = {\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.344 (sec). Leaf size: 26
dsolve([diff(y(t),t)=sqrt(y(t)^2-1),y(0) = 1/2],y(t), singsol=all)
\[ y \left (t \right ) = \frac {i \sqrt {3}\, {\mathrm e}^{t}}{4}-\frac {i \sqrt {3}\, {\mathrm e}^{-t}}{4}+\frac {{\mathrm e}^{t}}{4}+\frac {{\mathrm e}^{-t}}{4} \]
✓ Solution by Mathematica
Time used: 0.076 (sec). Leaf size: 59
DSolve[{y'[t]==Sqrt[y[t]^2-1],{y[0]==1/2}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {e^{-t} \sqrt {4 e^{2 t}+i \left (\sqrt {3}+i\right ) e^{4 t}-1-i \sqrt {3}}}{2 \sqrt {2}} \]