There exists a general formula for the following linear SDE

Question

I was reading a book about SDE and I encountered the following equation: $$d\vec{X} = (\vec{A}(t) + \vec{B}(t)\vec{X})dt + (\vec{C}(t) + \vec{F}(t)\vec{X})d\vec{W},$$ $$\vec{X} = \vec{X}_0.$$ The book only gives the solution only to the case where $\vec{B}$ is constant and $\vec{F} = 0$, i. e., $$d\vec{X} = (\vec{A}(t) + \vec{B}\vec{X})dt + \vec{C}(t)d\vec{W}.$$ I am interested in finding the solution to the following problem: $$dX_1 = dt + dW_1,$$ $$dX_2 = X_1dW_2.$$ I was wondering if anyone could tell me if there is a explicit formula for the first equation or how to solve the problem that I propose as the book doesn't tell how to find the solution to the problem or doesn't give any example on the method of solution for a system.