Internal problem ID [12960]
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(ii).
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 (-1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 1.672 (sec). Leaf size: 79
dsolve([diff(y(t),t)=cos( y(t)),y(-1) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \arctan \left (\frac {\sin \left (1\right ) {\mathrm e}^{2+2 t}+{\mathrm e}^{2+2 t}+\sin \left (1\right )-1}{\sin \left (1\right ) {\mathrm e}^{2+2 t}+{\mathrm e}^{2+2 t}-\sin \left (1\right )+1}, \frac {2 \,{\mathrm e}^{t +1} \cos \left (1\right )}{\sin \left (1\right ) {\mathrm e}^{2+2 t}+{\mathrm e}^{2+2 t}-\sin \left (1\right )+1}\right ) \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 13
DSolve[{y'[t]==Cos[ y[t]],{y[-1]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \arcsin \left (\coth \left (t+1+\coth ^{-1}(\sin (1))\right )\right ) \]