Returning implicit solution instead of explicit solution?

I tried solving a differential equation

I wrote the code

    syms  y(x) 
    ode = diff(y,x) == ((y/x)*cos(y/x))/((x/y).*sin(y/x)+cos(y/x))
    ySol(x)= dsolve(ode)

The software is returning implicit solution instead of explicit one but I tried it on Wolfram but it returned an explicit solution. Please help me..

Answer 1

[Walter Roberson]

Wolfram Alpha does not return an explicit solution for this.

http://www.wolframalpha.com/input/?i=solve+diff(y,x)+%3D%3D+((y%2Fx)*cos(y%2Fx))%2F((x%2Fy)*sin(y%2Fx)%2Bcos(y%2Fx))

It returns Log[Sin[y[x]/x]] + Log[y[x]/x] == -Log[x] + Subscript[c, 1]

which is an implicit solution.

[Karan Gill]

Additional comment: I think the implicit solution from dsolve could be more helpful. Will follow up on this.

[Gopalkrishna Pai]

Please give program code such that warning does not appear

[Walter Roberson]

The code such that the warning does not appear would just consist of turning the warning off, running the same program as above and failing to get a useful solution, and then turning the warning back on again.

Either the ODE has no explicit solution, or else the explicit solution is beyond the abilities of MATLAB, Maple, and Mathematica.