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 : Wednesday, March 05, 2025 at 04:02:51 AM
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*}

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

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

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

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

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

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

✓ Sympy. Time used: 1.706 (sec). Leaf size: 66

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sin(x)*cos(y(x)) + Derivative(y(x), x),0) 
ics = {y(1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \pi - \operatorname {asin}{\left (\frac {e^{2 \cos {\left (x \right )}} - e^{2 \cos {\left (1 \right )}}}{- e^{2 \cos {\left (x \right )}} - e^{2 \cos {\left (1 \right )}}} \right )}, \ y{\left (x \right )} = \operatorname {asin}{\left (\frac {e^{2 \cos {\left (x \right )}} - e^{2 \cos {\left (1 \right )}}}{- e^{2 \cos {\left (x \right )}} - e^{2 \cos {\left (1 \right )}}} \right )}\right ] \]