1.26 problem 26

Internal problem ID [4986]

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]

Solve \begin {gather*} \boxed {y^{\prime }-\cos \left (x -y\right )=0} \end {gather*}

Solution by Maple

Time used: 0.094 (sec). Leaf size: 16

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

\[ y \relax (x ) = x -2 \arctan \left (\frac {1}{c_{1}-x}\right ) \]

Solution by Mathematica

Time used: 0.593 (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*}