44.5.59 problem 49

Internal problem ID [7121]
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 : 49
Date solved : Sunday, March 30, 2025 at 11:43:13 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {1}{1+\sin \left (x \right )} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=diff(y(x),x) = 1/(sin(x)+1); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {2}{\tan \left (\frac {x}{2}\right )+1}+c_1 \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 31

ode=D[y[x],x]==1/(1+Sin[x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {2 \sin \left (\frac {x}{2}\right )}{\sin \left (\frac {x}{2}\right )+\cos \left (\frac {x}{2}\right )}+c_1 \]

✓ Sympy. Time used: 0.262 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = C_{1} - \frac {2}{\tan {\left (\frac {x}{2} \right )} + 1} \]