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 : Monday, January 27, 2025 at 02:46:57 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 16

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

\[ y = \arccos \left (\frac {x}{2}+c_{1} +\frac {\sin \left (2 x \right )}{4}\right ) \]

✓ Solution by Mathematica

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

DSolve[Csc[y[x]]+Sec[x]^2*D[y[x],x]==0,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*}