Internal problem ID [13002]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-\sin \left (y\right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 46
dsolve(diff(y(x),x)=sin(y(x)),y(x), singsol=all)
\[ y = \arctan \left (\frac {2 \,{\mathrm e}^{x} c_{1}}{{\mathrm e}^{2 x} c_{1}^{2}+1}, -\frac {{\mathrm e}^{2 x} c_{1}^{2}-1}{{\mathrm e}^{2 x} c_{1}^{2}+1}\right ) \]
✓ Solution by Mathematica
Time used: 0.293 (sec). Leaf size: 44
DSolve[y'[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*}