26.3.8 problem Exact Differential equations. Exercise 9.11, page 79

Internal problem ID [6941]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 9
Problem number : Exact Differential equations. Exercise 9.11, page 79
Date solved : Tuesday, September 30, 2025 at 04:07:05 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 20

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

\[ \sin \left (x \right ) y+x^{2}+y^{2}+\cos \left (y\right )+c_1 = 0 \]

✓ Mathematica. Time used: 0.129 (sec). Leaf size: 57

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

\[ \text {Solve}\left [\int _1^x(2 K[1]+\cos (K[1]) y(x))dK[1]+\int _1^{y(x)}\left (2 K[2]+\sin (x)-\sin (K[2])-\int _1^x\cos (K[1])dK[1]\right )dK[2]=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out