$dY_1 =\beta_1dt +1dB_1+2dB_2+3dB_3$
$dY_2 =\beta_2dt +1dB_1+2dB_2+2dB_3$
$\beta_{1,2} $ bounded, $B_{1,2,3}$ Brownian Motions.
System of SDEs.
I know how to solve a linear SDE with 1 Brownian motion.
I can (or at least think) solve a system of $n\times n$ linear SDEs.
But what am I supposed to do with 3 different Brownian Motions?
Indeed as mentioned in the comments, these are simply two correlated Itô diffusions since they have common Brownian motion noise, which you can actually combine into single Brownian motion $\sqrt{1+2^{2}+3^{2}}B_{t}=\sqrt{14}B_{t}.$