85.33.29 problem 29

Internal problem ID [22652]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 65
Problem number : 29
Date solved : Thursday, October 02, 2025 at 09:02:46 PM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Maple. Time used: 0.014 (sec). Leaf size: 20

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

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

✓ Mathematica. Time used: 0.105 (sec). Leaf size: 23

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

\[ \text {Solve}\left [x=\frac {1}{2} y(x)^2 \csc (y(x))+c_1 \csc (y(x)),y(x)\right ] \]

✓ Sympy. Time used: 2.956 (sec). Leaf size: 15

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

\[ C_{1} + x \sin {\left (y{\left (x \right )} \right )} - \frac {y^{2}{\left (x \right )}}{2} = 0 \]