10.5.17 problem 22

Internal problem ID [1209]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.6. Page 100
Problem number : 22
Date solved : Saturday, March 29, 2025 at 10:47:25 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 16

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

\[ y = \arcsin \left (\frac {{\mathrm e}^{-x}}{c_1 \,x^{2}}\right ) \]

✓ Mathematica. Time used: 45.553 (sec). Leaf size: 23

ode=(2+x)*Sin[y[x]]+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^{-x+c_1}}{x^2}\right ) \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.440 (sec). Leaf size: 26

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

\[ \left [ y{\left (x \right )} = \pi - \operatorname {asin}{\left (\frac {C_{1} e^{- x}}{x^{2}} \right )}, \ y{\left (x \right )} = \operatorname {asin}{\left (\frac {C_{1} e^{- x}}{x^{2}} \right )}\right ] \]