For what condition the following differential equation has unique solution

Question

Let me define it first
We have a differential equation $\frac{dx}{dt}=A(t)x(t)+B(t)u(t)+f(x(t),u(t),t)$
where $X=(x_1,x_2,.....,x_n)$, $A(t) \mbox{ and } B(t)$ is an $n\times n $ variable matrix,$u(t)=(u_1(t),u_2(t),....,u_n(t))$, I want condition of $f(x(t),u(t),t)$ such the given differential equation has a unique solution.I have read somewhere that if $f(x(t),u(t),t)$ satisfy the lipschitz condition with respect to $x$ and $u$ then this differential equation will have uniques solution but I don't have any idea that how to get this.If someone can help or give some hint that will be helpful.Thanks.