What will be the solution to the $n$ dimensional ODE of the form

Question

I am trying to figure out but am unable to. Any insight would be greatly appreciated.

What will be the solution to the $n$ dimensional ODE of the form

$$dX_i(t)= \sum_{j=1}^nf_{ij}(t)X_j(t) $$ with $X_i(0)=1, i=1, \cdots,n$. Here $X=(X_1,\cdots, X_{n})$ where $X_i$ is one dimensional for every $i$. $f=(f_1, \cdots,f_n)$ with $f_{ij}:\mathbb{R} \rightarrow \mathbb{R}^+\cup\{0\}$ for every $i,j$.