Internal problem ID [12612]
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 1.4 page 61
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-\sin \left (y\right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.609 (sec). Leaf size: 63
dsolve([diff(y(t),t)=sin(y(t)),y(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \arctan \left (-\frac {2 \,{\mathrm e}^{t} \sin \left (1\right )}{\left (-1+\cos \left (1\right )\right ) {\mathrm e}^{2 t}-\cos \left (1\right )-1}, \frac {\left (1-\cos \left (1\right )\right ) {\mathrm e}^{2 t}-\cos \left (1\right )-1}{\left (-1+\cos \left (1\right )\right ) {\mathrm e}^{2 t}-\cos \left (1\right )-1}\right ) \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 16
DSolve[{y'[t]==Sin[y[t]],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \arccos (-\tanh (t-\text {arctanh}(\cos (1)))) \]