Internal problem ID [12639]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 1. First-Order Differential Equations. Exercises section 1.6 page 89
Problem number: 3 and 15(i).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-\cos \left (y\right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 32
dsolve([diff(y(t),t)=cos( y(t)),y(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \arctan \left (\frac {{\mathrm e}^{2 t}-1}{{\mathrm e}^{2 t}+1}, \frac {2 \,{\mathrm e}^{t}}{{\mathrm e}^{2 t}+1}\right ) \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 8
DSolve[{y'[t]==Cos[ y[t]],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \arcsin (\tanh (t)) \]