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: 31.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {y^{\prime }+\sin \left (y+x \right )^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 16
dsolve(diff(y(x),x)+sin(x+y(x))^2=0,y(x), singsol=all)
\[ y \left (x \right ) = -x -\arctan \left (-x +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.203 (sec). Leaf size: 27
DSolve[y'[x]+Sin[x+y[x]]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}[2 (\tan (y(x)+x)-\arctan (\tan (y(x)+x)))+2 y(x)=c_1,y(x)] \]