Question: Transcendental equations system

First of all: I'm so sorry, I posted my question to a wrong place ( into the poll).

So I copy here the question and the answer of jakubi and my reply to jakubi.

Question:

I would like to solve the following system

x*(2*sin(x)*y^2+x^3*cos(x)+x*cos(x)*y^2) = y*(2*sin(y)*x^2+y*cos(y)*x^2+y^3*cos(y)),

-x*sin(x) = y*sin(y);

Until I have founded only the solutions

x = k*Pi,  y = +/- k*Pi;    k is any integer.

jakubi's answer:

more solutions

eq:=x*(2*sin(x)*y^2+x^3*cos(x)+x*cos(x)*y^2) = 
y*(2*sin(y)*x^2+y*cos(y)*x^2+y^3*cos(y)),
-x*sin(x) = y*sin(y):

eval({eq},x = y*I);
                                    3               3
         {y sinh(y) = y sin(y), -2 y  sinh(y) = -2 y  sin(y)}


eval({eq},x = -y*I);

                                    3               3
         {y sinh(y) = y sin(y), -2 y  sinh(y) = -2 y  sin(y)}

My reply:

I forgot to say that x and y are real numbers. (Sorry.)