64.4.16 problem 16

Internal problem ID [13234]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number : 16
Date solved : Monday, March 31, 2025 at 07:42:27 AM
CAS classification : [_separable]

\begin{align*} 8 \cos \left (y\right )^{2}+\csc \left (x \right )^{2} y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (\frac {\pi }{12}\right )&=\frac {\pi }{4} \end{align*}

✓ Maple. Time used: 0.228 (sec). Leaf size: 20

ode:=8*cos(y(x))^2+csc(x)^2*diff(y(x),x) = 0; 
ic:=y(1/12*Pi) = 1/4*Pi; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\arctan \left (-\frac {\pi }{3}+4 x -2 \sin \left (2 x \right )\right ) \]

✓ Mathematica. Time used: 0.188 (sec). Leaf size: 79

ode=(8*Cos[y[x]]^2)+Csc[x]^2*D[y[x],x]==0; 
ic={y[Pi/12]==Pi/4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [-y(x) \int _{\frac {\pi }{12}}^x0dK[1]+\int _{\frac {\pi }{12}}^x-\left ((2 \cos (2 K[1])+\cos (2 K[1]-2 y(x))-2 \cos (2 y(x))+\cos (2 K[1]+2 y(x))-2) \sec ^2(y(x))\right )dK[1]+\tan (y(x))=1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(8*cos(y(x))**2 + Derivative(y(x), x)/sin(x)**2,0) 
ics = {y(pi/12): pi/4} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out