78.1.13 problem 1 (n)

Internal problem ID [17997]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 1 (n)
Date solved : Monday, March 31, 2025 at 04:56:01 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 15

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

\[ x -c_1 y-\sin \left (y\right ) = 0 \]

✓ Mathematica. Time used: 0.226 (sec). Leaf size: 14

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

\[ \text {Solve}[x=\sin (y(x))+c_1 y(x),y(x)] \]

✓ Sympy. Time used: 4.442 (sec). Leaf size: 15

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

\[ C_{1} + \frac {x}{y{\left (x \right )}} - \frac {\sin {\left (y{\left (x \right )} \right )}}{y{\left (x \right )}} = 0 \]