20.5.12 problem Problem 12

Internal problem ID [3695]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.9, Exact Differential Equations. page 91
Problem number : Problem 12
Date solved : Sunday, March 30, 2025 at 02:05:56 AM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.015 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.129 (sec). Leaf size: 17

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

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

✗ Sympy

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

Timed Out