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 : Sunday, March 30, 2025 at 12:37:48 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*}

✓ Maple. Time used: 0.116 (sec). Leaf size: 10

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

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

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

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

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

✓ Sympy. Time used: 0.438 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-1/sin(y(x)) + Derivative(y(x), x)/sin(x),0) 
ics = {y(pi/2): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \operatorname {acos}{\left (\cos {\left (x \right )} + \cos {\left (1 \right )} \right )} \]