47.1.31 problem 31

Internal problem ID [7412]
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
Date solved : Monday, January 27, 2025 at 02:53:22 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }+\sin \left (x +y\right )^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 16

dsolve(diff(y(x),x)+sin(x+y(x))^2=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.197 (sec). Leaf size: 27

DSolve[D[y[x],x]+Sin[x+y[x]]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

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