Internal problem ID [2654]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-\left (\sin ^{2}\left (x -y\right )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve(diff(y(x),x)=sin(x-y(x))^2,y(x), singsol=all)
\[ y \relax (x ) = x +\arctan \left (-x +c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.228 (sec). Leaf size: 31
DSolve[y'[x]==Sin[x-y[x]]^2,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}[2 y(x)-2 (\tan (x-y(x))-\text {ArcTan}(\tan (x-y(x))))=c_1,y(x)] \]