Let $a_0, \ldots , a_{n-1}$ continuous functions in an interval $I$.Consider the equation $$x^{(n)} = a_{n-1}(t)x^{(n-1)}+\cdots+a_0(t)x. \tag 1$$
Let $\phi_1, \phi_2, \ldots,\phi_n$ $n$ are functions of $C^n$ such that $W(\phi_1, \phi_2, \ldots ,\phi_n)(t) \neq 0$ in I. Prove that there is a unique equation of the form (1) which $ \phi_1, \phi_2, \ldots,\phi_n $ is based solutions. ($W$ denotes the Wronskian)
Showed that $\phi_1, \phi_2, \ldots,\phi_n$ are linearly independent if $W \neq 0$, but I'm not finishing.