44.1.13 problem 1(n)

Internal problem ID [9071]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS. Page 9
Problem number : 1(n)
Date solved : Tuesday, September 30, 2025 at 06:03:42 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: 0.007 (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: 0.15 (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: 2.772 (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)
 

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