89.3.13 problem 13

Internal problem ID [24311]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 34
Problem number : 13
Date solved : Thursday, October 02, 2025 at 10:14:22 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} x +\sin \left (y\right )-\cos \left (y\right )-x \cos \left (y\right ) \left (2 x \sin \left (y\right )+1\right ) y^{\prime }&=0 \end{align*}

✗ Maple

ode:=x+sin(y(x))-cos(y(x))-x*cos(y(x))*(2*x*sin(y(x))+1)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=( x+Sin[y[x]]-Cos[y[x]]  )- x*Cos[y[x]]*(2*x*Sin[y[x]]+1 )*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*(2*x*sin(y(x)) + 1)*cos(y(x))*Derivative(y(x), x) + x + sin(y(x)) - cos(y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out