47.1.30 problem 30

Internal problem ID [7411]
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
Date solved : Monday, January 27, 2025 at 02:53:19 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\cos \left (x -y-1\right ) \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 15

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

\[ y = x -1-2 \,\operatorname {arccot}\left (-x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 5.799 (sec). Leaf size: 59

DSolve[D[y[x],x]==Cos[x-y[x]-1],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -i \log \left (\frac {e^{i (x-1)} (2 x-c_1)}{2 x-4 i-c_1}\right ) \\ y(x)\to -i \log \left (e^{i (x-1)}\right ) \\ \end{align*}