67.1.5 problem Problem 1(e)

Internal problem ID [13952]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 2, First Order Equations. Problems page 149
Problem number : Problem 1(e)
Date solved : Tuesday, January 28, 2025 at 06:09:31 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.087 (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: 0.824 (sec). Leaf size: 59

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

\begin{align*} y(x)\to -x+2 \arctan \left (x+\frac {c_1}{2}\right ) \\ y(x)\to -x+2 \arctan \left (x+\frac {c_1}{2}\right ) \\ y(x)\to -x-\pi \\ y(x)\to \pi -x \\ \end{align*}