Internal problem ID [4991]
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: 31.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }+\sin ^{2}\left (x +y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.036 (sec). Leaf size: 16
dsolve(diff(y(x),x)+sin(x+y(x))^2=0,y(x), singsol=all)
\[ y \relax (x ) = -x -\arctan \left (c_{1}-x \right ) \]
✓ Solution by Mathematica
Time used: 0.198 (sec). Leaf size: 27
DSolve[y'[x]+Sin[x+y[x]]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}[2 (\tan (y(x)+x)-\text {ArcTan}(\tan (y(x)+x)))+2 y(x)=c_1,y(x)] \]