64.4.16 problem 16

Internal problem ID [13305]
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 : Tuesday, January 28, 2025 at 05:17:22 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*}

✓ Solution by Maple

Time used: 0.230 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

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

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

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