73.1.2 problem 2.2 (b)

Internal problem ID [14980]
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)
Date solved : Tuesday, January 28, 2025 at 07:26:09 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=3-\sin \left (y\right ) \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 22

dsolve(diff(y(x),x)=3-sin(y(x)),y(x), singsol=all)
 

\[ y = 2 \arctan \left (\frac {1}{3}+\frac {2 \sqrt {2}\, \tan \left (\left (x +c_{1} \right ) \sqrt {2}\right )}{3}\right ) \]

✓ Solution by Mathematica

Time used: 0.207 (sec). Leaf size: 34

DSolve[D[y[x],x]==3-Sin[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{\sin (K[1])-3}dK[1]\&\right ][-x+c_1] \\ y(x)\to \arcsin (3) \\ \end{align*}