73.7.19 problem 19

Internal problem ID [15098]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 19
Date solved : Thursday, March 13, 2025 at 05:37:52 AM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Maple. Time used: 0.583 (sec). Leaf size: 16

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

\[ y+x +\cot \left (y\right )-\csc \left (y\right ) c_{1} = 0 \]

✓ Mathematica. Time used: 0.162 (sec). Leaf size: 31

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

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

✓ Sympy. Time used: 8.886 (sec). Leaf size: 22

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

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