59.5.3 problem 10.1 (iii)

Internal problem ID [15023]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 10, Two tricks for nonlinear equations. Exercises page 97
Problem number : 10.1 (iii)
Date solved : Thursday, October 02, 2025 at 10:01:24 AM
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: 0.015 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.106 (sec). Leaf size: 17

ode=(x*Cos[y[x]]+Cos[x])*D[y[x],x]+Sin[y[x]]-y[x]*Sin[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