Internal problem ID [4985]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page
7
Problem number: 26.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {y^{\prime }-\cos \left (-y+x \right )=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 16
dsolve(diff(y(x),x)=cos(y(x)-x),y(x), singsol=all)
\[ y \left (x \right ) = x -2 \arctan \left (\frac {1}{-x +c_{1}}\right ) \]
✓ Solution by Mathematica
Time used: 0.425 (sec). Leaf size: 40
DSolve[y'[x]==Cos[y[x]-x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+2 \cot ^{-1}\left (x-\frac {c_1}{2}\right ) \\ y(x)\to x+2 \cot ^{-1}\left (x-\frac {c_1}{2}\right ) \\ y(x)\to x \\ \end{align*}