44.4.16 problem 4 (d)

Internal problem ID [7029]
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 (d)
Date solved : Monday, January 27, 2025 at 02:41:32 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 (0\right )&=-{\frac {5}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.483 (sec). Leaf size: 73

dsolve([diff(y(x),x)=sin(x)*cos(y(x)),y(0) = -5/2],y(x), singsol=all)
 

\[ y = \arctan \left (\frac {\left (-1+\sin \left (\frac {5}{2}\right )\right ) {\mathrm e}^{2-2 \cos \left (x \right )}+\sin \left (\frac {5}{2}\right )+1}{\left (-1+\sin \left (\frac {5}{2}\right )\right ) {\mathrm e}^{2-2 \cos \left (x \right )}-1-\sin \left (\frac {5}{2}\right )}, -\frac {2 \,{\mathrm e}^{1-\cos \left (x \right )} \cos \left (\frac {5}{2}\right )}{\left (-1+\sin \left (\frac {5}{2}\right )\right ) {\mathrm e}^{2-2 \cos \left (x \right )}-1-\sin \left (\frac {5}{2}\right )}\right ) \]

✓ Solution by Mathematica

Time used: 0.115 (sec). Leaf size: 26

DSolve[{D[y[x],x]==Sin[x]*Cos[y[x]],{y[0]==-5/2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 \arctan \left (\tanh \left (-\text {arctanh}\left (\tan \left (\frac {5}{4}\right )\right )-\frac {\cos (x)}{2}+\frac {1}{2}\right )\right ) \]