83.4.5 problem 1 (e)

Internal problem ID [21932]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter III. First order differential equations of the first degree. Ex. V at page 42
Problem number : 1 (e)
Date solved : Thursday, October 02, 2025 at 08:15:01 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 17

ode:=sin(x)+sin(y(x))+(x*cos(y(x))+cos(y(x)))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \arcsin \left (\frac {\cos \left (x \right )-c_1}{1+x}\right ) \]

✓ Mathematica. Time used: 11.144 (sec). Leaf size: 17

ode=(Sin[x]+Sin[y[x]]  )+(x*Cos[y[x]]+Cos[y[x]] )*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \arcsin \left (\frac {\cos (x)+c_1}{x+1}\right ) \end{align*}

✓ Sympy. Time used: 3.055 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x*cos(y(x)) + cos(y(x)))*Derivative(y(x), x) + sin(x) + sin(y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \operatorname {asin}{\left (\frac {C_{1} - \cos {\left (x \right )}}{x + 1} \right )} + \pi , \ y{\left (x \right )} = - \operatorname {asin}{\left (\frac {C_{1} - \cos {\left (x \right )}}{x + 1} \right )}\right ] \]