1.30 problem 30

Internal problem ID [4990]

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]

Solve \begin {gather*} \boxed {y^{\prime }-\cos \left (x -y-1\right )=0} \end {gather*}

Solution by Maple

Time used: 0.043 (sec). Leaf size: 17

dsolve(diff(y(x),x)=cos(x-y(x)-1),y(x), singsol=all)
 

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

Solution by Mathematica

Time used: 0.441 (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*}