83.4.5 problem 5

Internal problem ID [18998]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (C) at page 12
Problem number : 5
Date solved : Thursday, March 13, 2025 at 01:19:07 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Maple. Time used: 0.092 (sec). Leaf size: 18

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

\[ y \left (x \right ) = x \operatorname {RootOf}\left (\textit {\_Z} \cos \left (\textit {\_Z} \right ) x^{2}-c_{1} \right ) \]

✓ Mathematica. Time used: 0.32 (sec). Leaf size: 31

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

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

✗ Sympy

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

Timed Out