78.3.4 problem 1 (d)

Internal problem ID [18028]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 7 (Homogeneous Equations). Problems at page 67
Problem number : 1 (d)
Date solved : Thursday, March 13, 2025 at 11:21:04 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 15

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

\[ y = \left (\frac {\pi }{2}+\arcsin \left (\ln \left (x \right )+c_1 \right )\right ) x \]

✓ Mathematica. Time used: 0.406 (sec). Leaf size: 34

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

\begin{align*} y(x)\to -x \arccos (-\log (x)-c_1) \\ y(x)\to x \arccos (-\log (x)-c_1) \\ \end{align*}

✓ Sympy. Time used: 0.873 (sec). Leaf size: 24

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

\[ \left [ y{\left (x \right )} = x \left (- \operatorname {acos}{\left (C_{1} - \log {\left (x \right )} \right )} + 2 \pi \right ), \ y{\left (x \right )} = x \operatorname {acos}{\left (C_{1} - \log {\left (x \right )} \right )}\right ] \]