44.4.14 problem 4 (b)

Internal problem ID [7027]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.1 Solution curves without a solution. Exercises 2.1 at page 44
Problem number : 4 (b)
Date solved : Monday, January 27, 2025 at 02:41:24 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.133 (sec). Leaf size: 56

dsolve([diff(y(x),x)=sin(x)*cos(y(x)),y(1) = 0],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.126 (sec). Leaf size: 20

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

\[ y(x)\to 2 \arctan \left (\tanh \left (\frac {1}{2} (\cos (1)-\cos (x))\right )\right ) \]