50.8.12 problem 2(d)

Internal problem ID [7928]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Problems for Review and Discovery. Page 53
Problem number : 2(d)
Date solved : Monday, January 27, 2025 at 03:32:46 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{2}\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.079 (sec). Leaf size: 10

dsolve([csc(x)*diff(y(x),x)=csc(y(x)),y(1/2*Pi) = 1],y(x), singsol=all)
 

\[ y = \arccos \left (\cos \left (x \right )+\cos \left (1\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.388 (sec). Leaf size: 11

DSolve[{Csc[x]*D[y[x],x]==Csc[y[x]],{y[Pi/2]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \arccos (\cos (x)+\cos (1)) \]