Internal problem ID [5743]
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: 30.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {y^{\prime }-\cos \left (x -y-1\right )=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 17
dsolve(diff(y(x),x)=cos(x-y(x)-1),y(x), singsol=all)
\[ y \left (x \right ) = x -1-2 \arctan \left (\frac {1}{-x +c_{1}}\right ) \]
✓ Solution by Mathematica
Time used: 0.551 (sec). Leaf size: 50
DSolve[y'[x]==Cos[x-y[x]-1],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x-2 \cot ^{-1}\left (-x+1+\frac {c_1}{2}\right )-1 y(x)\to x-2 \cot ^{-1}\left (-x+1+\frac {c_1}{2}\right )-1 y(x)\to x-1 \end{align*}