Internal problem ID [2499]
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]
\[ \boxed {y^{\prime }-\tan \left (x \right ) \cos \left (y\right ) \left (\cos \left (y\right )+\sin \left (y\right )\right )=0} \]
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 18
dsolve(diff(y(x),x) = tan(x)*cos(y(x))*( cos(y(x)) + sin(y(x)) ),y(x), singsol=all)
\[ y \left (x \right ) = -\arctan \left (\frac {\cos \left (x \right )-c_{1}}{\cos \left (x \right )}\right ) \]
✓ Solution by Mathematica
Time used: 60.547 (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 -\arccos \left (-\frac {\cos (x)}{\sqrt {\cos (2 x)-2 e^{\frac {c_1}{2}} \cos (x)+1+e^{c_1}}}\right ) y(x)\to \arccos \left (-\frac {\cos (x)}{\sqrt {\cos (2 x)-2 e^{\frac {c_1}{2}} \cos (x)+1+e^{c_1}}}\right ) y(x)\to -\arccos \left (\frac {\cos (x)}{\sqrt {\cos (2 x)-2 e^{\frac {c_1}{2}} \cos (x)+1+e^{c_1}}}\right ) y(x)\to \arccos \left (\frac {\cos (x)}{\sqrt {\cos (2 x)-2 e^{\frac {c_1}{2}} \cos (x)+1+e^{c_1}}}\right ) \end{align*}