89.6.20 problem 20

Internal problem ID [24403]
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. Miscellaneous Exercises at page 45
Problem number : 20
Date solved : Thursday, October 02, 2025 at 10:25:11 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.099 (sec). Leaf size: 17

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

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

✗ Sympy

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

Timed Out