ODE stiff and implicit

Hello,

I have a set of ODEs. They are stiff (ode15s-solver) and implicit (ode15i).

Example:

dXdt = dYdt * X^2/Y + dZdt * X;
dYdt = Y*X + dXdt * X + dZdt * Z;
dZdt = dXdt * Z;

The example shows the structure (dXdt = f(X,Y, dYdt, dZdt) ...). Im not able to solve the equations manually that I got the form

dXdt = f(X,Y,Z)
dYdt = f(X,Y,Z)
dZdt = f(X,Y,Z)

So I should use the implicit solver? But what to do, if the system is stiff?