65.5.3 problem 10.1 (iii)

Internal problem ID [13663]
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 : Wednesday, March 05, 2025 at 10:10:28 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.055 (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);
 

\[ \cos \left (x \right ) y+\sin \left (y\right ) x +c_{1} = 0 \]

✓ Mathematica. Time used: 0.173 (sec). Leaf size: 59

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]
 

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

✗ 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