How to apply nodal analysis when value of dependent voltage source depends on current of a plain wire?
In nodal analysis you can deal with current sources by simply including them in the equations you write rather than a voltage divided by resistance between nodes.

So if you had Vx and Vy connected by Rz your nodal equation for Vx would contain one term (along with others for other nodes connected) that is:

(Vx-Vy)/Rz + other terms = 0

Now imagine you had the current source Iw coming out of Vx also then you would have:

(Vx-Vy)/Rz + Iw + other terms = 0

Now imagine that Vx was connected to Vu through dependant source Va=5*Iw

Your set of equations (assuming no other nodes or connections) may be:

(Vx-Vy)/Rz + Iw = 0

Vx-Vu = Va

Va = 5*Iw

NOTE: This is an example and does not represent a complete set of nodal equation, if it were there would be n equations and n unknowns (easily solved with matrices)