73.7.20 problem 20

Internal problem ID [15099]
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 : 20
Date solved : Thursday, March 13, 2025 at 05:37:57 AM
CAS classification : [_separable]

\begin{align*} \sin \left (y\right )+\left (1+x \right ) \cos \left (y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.041 (sec). Leaf size: 14

ode:=sin(y(x))+(1+x)*cos(y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \arcsin \left (\frac {1}{c_{1} \left (x +1\right )}\right ) \]

✓ Mathematica. Time used: 17.623 (sec). Leaf size: 21

ode=Sin[y[x]]+(1+x)*Cos[y[x]]*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \arcsin \left (\frac {e^{c_1}}{x+1}\right ) \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.394 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + 1)*cos(y(x))*Derivative(y(x), x) + sin(y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \pi - \operatorname {asin}{\left (\frac {C_{1}}{x + 1} \right )}, \ y{\left (x \right )} = \operatorname {asin}{\left (\frac {C_{1}}{x + 1} \right )}\right ] \]