72.3.4 problem 4

Internal problem ID [14668]
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
Date solved : Tuesday, January 28, 2025 at 06:46:58 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\sin \left (y\right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 1.911 (sec). Leaf size: 63

dsolve([diff(y(t),t)=sin(y(t)),y(0) = 1],y(t), singsol=all)
 

\[ y = \arctan \left (-\frac {2 \,{\mathrm e}^{t} \sin \left (1\right )}{\left (-1+\cos \left (1\right )\right ) {\mathrm e}^{2 t}-\cos \left (1\right )-1}, \frac {\left (1-\cos \left (1\right )\right ) {\mathrm e}^{2 t}-\cos \left (1\right )-1}{\left (-1+\cos \left (1\right )\right ) {\mathrm e}^{2 t}-\cos \left (1\right )-1}\right ) \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 16

DSolve[{D[y[t],t]==Sin[y[t]],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \arccos (-\tanh (t-\text {arctanh}(\cos (1)))) \]