73.3.24 problem 4.6 (d)

Internal problem ID [15058]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.6 (d)
Date solved : Tuesday, January 28, 2025 at 07:29:04 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 46

dsolve(diff(y(x),x)=sin(y(x)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.281 (sec). Leaf size: 44

DSolve[D[y[x],x]==Sin[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\arccos (-\tanh (x+c_1)) \\ y(x)\to \arccos (-\tanh (x+c_1)) \\ y(x)\to 0 \\ y(x)\to -\pi \\ y(x)\to \pi \\ \end{align*}