How to integrate a multi dimensional SDE forced by the same source of noise?

Hi everyone for my research I need to integrate an SDE system of this kind:

dx=f1(x,y)dt + g1(x,y)dW
dy=f2(x,y)dt + g2(x,y)dW

My issue is that I want the Winer noise dW to be exactly the same for the two variable. I wanted to take advantage over DifferentialEquation.jl but I can really find in the documentation the way to specify this particular case to SDEProblem. I’m sure it must be related to the option NoiseProcess but I had no luck.
Thanks for your help!

That’s a scalar noise SDE. There is an example of this in the tutorials.