18.1.14 problem Problem 14.16

Internal problem ID [3470]
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
Date solved : Monday, January 27, 2025 at 07:38:07 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\tan \left (x \right ) \cos \left (y\right ) \left (\cos \left (y\right )+\sin \left (y\right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.196 (sec). Leaf size: 11

dsolve(diff(y(x),x) = tan(x)*cos(y(x))*( cos(y(x)) + sin(y(x)) ),y(x), singsol=all)
 

\[ y \left (x \right ) = \arctan \left (-1+\sec \left (x \right ) c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 60.475 (sec). Leaf size: 143

DSolve[D[y[x],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*}