Internal problem ID [10611]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {8 \cos \left (y\right )^{2}+\csc \left (x \right )^{2} y^{\prime }=0} \] With initial conditions \begin {align*} \left [y \left (\frac {\pi }{12}\right ) = \frac {\pi }{4}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.234 (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)
\[ y \left (x \right ) = -\arctan \left (-\frac {\pi }{3}+4 x -2 \sin \left (2 x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.752 (sec). Leaf size: 21
DSolve[{(8*Cos[y[x]]^2)+Csc[x]^2*y'[x]==0,{y[Pi/12]==Pi/4}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \arctan \left (-4 x+2 \sin (2 x)+\frac {\pi }{3}\right ) \\ \end{align*}