Internal problem ID [13244]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 2. Integration and differential equations. Additional exercises. page
32
Problem number: 2.2 (b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }+\sin \left (y\right )=3} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve(diff(y(x),x)=3-sin(y(x)),y(x), singsol=all)
\[ y \left (x \right ) = 2 \arctan \left (\frac {1}{3}+\frac {2 \sqrt {2}\, \tan \left (\left (c_{1} +x \right ) \sqrt {2}\right )}{3}\right ) \]
✓ Solution by Mathematica
Time used: 5.504 (sec). Leaf size: 83
DSolve[y'[x]==3-Sin[y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 \arctan \left (\frac {1}{3} \left (-1-2 \sqrt {2} \tan \left (\sqrt {2} (x-c_1)\right )\right )\right ) \\ y(x)\to 2 \arctan \left (\frac {1}{3} \left (1+2 \sqrt {2} \tan \left (\sqrt {2} (x-c_1)\right )\right )\right ) \\ y(x)\to \arcsin (3) \\ y(x)\to \text {Interval}[\{-\pi ,\pi \}] \\ \end{align*}