15.8.10 problem 10

Internal problem ID [3013]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 10
Date solved : Sunday, March 30, 2025 at 01:05:54 AM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.023 (sec). Leaf size: 25

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

\[ -\cos \left (x \right ) y-2 x \cos \left (y\right )-\ln \left (\cos \left (x \right )\right )+\cos \left (y\right )+c_1 = 0 \]

✓ Mathematica. Time used: 0.702 (sec). Leaf size: 29

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

\[ \text {Solve}[4 x \cos (y(x))-2 \cos (y(x))+2 y(x) \cos (x)+2 \log (\cos (x))=c_1,y(x)] \]

✗ Sympy

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

Timed Out