2.364   ODE No. 364

\[ x y'(x) \left (y(x) \sin \left (\frac {y(x)}{x}\right )-x \cos \left (\frac {y(x)}{x}\right )\right )-y(x) \left (y(x) \sin \left (\frac {y(x)}{x}\right )+x \cos \left (\frac {y(x)}{x}\right )\right )=0 \]

✓ Mathematica : cpu = 0.489657 (sec), leaf count = 31

DSolve[-(y[x]*(x*Cos[y[x]/x] + Sin[y[x]/x]*y[x])) + x*(-(x*Cos[y[x]/x]) + Sin[y[x]/x]*y[x])*Derivative[1][y][x] == 0,y[x],x]
 

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

✓ Maple : cpu = 0.161 (sec), leaf count = 23

dsolve((y(x)*sin(y(x)/x)-x*cos(y(x)/x))*x*diff(y(x),x)-(x*cos(y(x)/x)+y(x)*sin(y(x)/x))*y(x) = 0,y(x))
 

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