76.4.21 problem 27

Internal problem ID [17344]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.6 (Exact equations and integrating factors). Problems at page 100
Problem number : 27
Date solved : Monday, March 31, 2025 at 03:55:26 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 9

ode:=1/(x/y(x)-sin(y(x)))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ y &= c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.126 (sec). Leaf size: 32

ode=1+(x/y[x]-Sin[y[x]])*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [x=\frac {\int _1^{y(x)}K[1] \sin (K[1])dK[1]}{y(x)}+\frac {c_1}{y(x)},y(x)\right ] \]

✓ Sympy. Time used: 0.151 (sec). Leaf size: 3

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

\[ y{\left (x \right )} = C_{1} \]