35.4.11 problem 11

Internal problem ID [6129]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 4. OTHER METHODS FOR FIRST-ORDER EQUATIONS. page 406
Problem number : 11
Date solved : Monday, January 27, 2025 at 01:37:47 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 16

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

\[ y = -x -2 \arctan \left (-x +c_1 \right ) \]

✓ Solution by Mathematica

Time used: 25.963 (sec). Leaf size: 163

DSolve[D[y[x],x]==Cos[x+y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\arccos \left (\frac {4 (2 x-2 i+c_1) \sin (x)-\left (4 x^2+4 (c_1-2 i) x-8+c_1{}^2-4 i c_1\right ) \cos (x)}{(2 x+c_1) (2 x-4 i+c_1)}\right ) \\ y(x)\to \arccos \left (\frac {4 (2 x-2 i+c_1) \sin (x)-\left (4 x^2+4 (c_1-2 i) x-8+c_1{}^2-4 i c_1\right ) \cos (x)}{(2 x+c_1) (2 x-4 i+c_1)}\right ) \\ y(x)\to \pi -\arccos (\cos (x)) \\ y(x)\to \arccos (\cos (x))-\pi \\ \end{align*}