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 : Tuesday, February 04, 2025 at 12:15:48 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[D[y[x],x]==1/(1+Sin[x]),y[x],x,IncludeSingularSolutions -> True]
 

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