Internal problem ID [5507]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\csc \relax (x ) y^{\prime }-\csc \relax (y)=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {\pi }{2}\right ) = 1\right ] \end {align*}
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 10
dsolve([csc(x)*diff(y(x),x)=csc(y(x)),y(1/2*Pi) = 1],y(x), singsol=all)
\[ y \relax (x ) = \arccos \left (\cos \relax (x )+\cos \relax (1)\right ) \]
✓ Solution by Mathematica
Time used: 0.602 (sec). Leaf size: 11
DSolve[{Csc[x]*y'[x]==Csc[y[x]],{y[Pi/2]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {ArcCos}(\cos (x)+\cos (1)) \\ \end{align*}