84.11.2 problem 6.2

Internal problem ID [22139]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 6. Exact first-order differential equations. Solved problems. Page 24
Problem number : 6.2
Date solved : Thursday, October 02, 2025 at 08:31:37 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 21

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

\[ \frac {x^{2}}{2}+x \sin \left (y\right )-y^{2}+c_1 = 0 \]

✓ Mathematica. Time used: 0.091 (sec). Leaf size: 25

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

\[ \text {Solve}\left [\frac {x^2}{2}-y(x)^2+x \sin (y(x))=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out