Internal problem ID [1990]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number: Problem 14.16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\tan \relax (x ) \cos \relax (y) \left (\cos \relax (y)+\sin \relax (y)\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 18
dsolve(diff(y(x),x) = tan(x)*cos(y(x))*( cos(y(x)) + sin(y(x)) ),y(x), singsol=all)
\[ y \relax (x ) = -\arctan \left (\frac {\cos \relax (x )-c_{1}}{\cos \relax (x )}\right ) \]
✓ Solution by Mathematica
Time used: 60.366 (sec). Leaf size: 143
DSolve[y'[x]==Tan[x]*Cos[y[x]]*( Cos[y[x]] + Sin[y[x]] ),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sec ^{-1}\left (\sec (x) \left (-\sqrt {\cos (2 x)-2 e^{\frac {c_1}{2}} \cos (x)+1+e^{c_1}}\right )\right ) \\ y(x)\to \sec ^{-1}\left (\sec (x) \left (-\sqrt {\cos (2 x)-2 e^{\frac {c_1}{2}} \cos (x)+1+e^{c_1}}\right )\right ) \\ y(x)\to -\sec ^{-1}\left (\sec (x) \sqrt {\cos (2 x)-2 e^{\frac {c_1}{2}} \cos (x)+1+e^{c_1}}\right ) \\ y(x)\to \sec ^{-1}\left (\sec (x) \sqrt {\cos (2 x)-2 e^{\frac {c_1}{2}} \cos (x)+1+e^{c_1}}\right ) \\ \end{align*}