44.5.11 problem 11

Internal problem ID [7073]
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 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 11
Date solved : Sunday, March 30, 2025 at 11:37:43 AM
CAS classification : [_separable]

\begin{align*} \csc \left (y\right )+\sec \left (x \right )^{2} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 16

ode:=csc(y(x))+sec(x)^2*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \arccos \left (\frac {x}{2}+c_1 +\frac {\sin \left (2 x \right )}{4}\right ) \]

✓ Mathematica. Time used: 1.331 (sec). Leaf size: 43

ode=Csc[y[x]]+Sec[x]^2*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\arccos \left (\frac {1}{2} (x+\sin (x) \cos (x)-2 c_1)\right ) \\ y(x)\to \arccos \left (\frac {1}{2} (x+\sin (x) \cos (x)-2 c_1)\right ) \\ \end{align*}

✓ Sympy. Time used: 0.774 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x)/cos(x)**2 + 1/sin(y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \operatorname {acos}{\left (C_{1} + \frac {x}{2} + \frac {\sin {\left (2 x \right )}}{4} \right )} + 2 \pi , \ y{\left (x \right )} = \operatorname {acos}{\left (C_{1} + \frac {x}{2} + \frac {\sin {\left (2 x \right )}}{4} \right )}\right ] \]