32.1.10 problem First order with homogeneous Coefficients. Exercise 7.11, page 61

Internal problem ID [5780]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 7
Problem number : First order with homogeneous Coefficients. Exercise 7.11, page 61
Date solved : Sunday, March 30, 2025 at 10:15:56 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 49

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

\[ y = \operatorname {RootOf}\left ({\mathrm e}^{2 \textit {\_Z}} \left (4 \left (\ln \left (x \right )^{2}+2 c_1 \ln \left (x \right )+c_1^{2}\right ) {\mathrm e}^{2 \textit {\_Z}}-4 \sin \left (\textit {\_Z} \right ) \left (\ln \left (x \right )+c_1 \right ) {\mathrm e}^{\textit {\_Z}}+2 \sin \left (\textit {\_Z} \right )^{2}-1\right )\right ) x \]

✓ Mathematica. Time used: 0.326 (sec). Leaf size: 39

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

\[ \text {Solve}\left [-\frac {1}{2} e^{-\frac {y(x)}{x}} \left (\sin \left (\frac {y(x)}{x}\right )+\cos \left (\frac {y(x)}{x}\right )\right )=-\log (x)+c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out