87.5.9 problem 9

Internal problem ID [23302]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 47
Problem number : 9
Date solved : Thursday, October 02, 2025 at 09:29:15 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.09 (sec). Leaf size: 18

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

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

✗ Sympy

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

Timed Out