28.1.18 problem 18

Internal problem ID [4324]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 18
Date solved : Monday, January 27, 2025 at 09:02:39 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\sin \left (x -y\right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 12

dsolve(diff(y(x),x)=sin(x-y(x))^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.197 (sec). Leaf size: 31

DSolve[D[y[x],x]==Sin[x-y[x]]^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}[2 y(x)-2 (\tan (x-y(x))-\arctan (\tan (x-y(x))))=c_1,y(x)] \]