For three functions $\displaystyle f_1,\,f_2,\,f_3$, the wronskian is $\displaystyle W(x)=\left| \begin{array}{ccc} f_1(x) & f_2(x) & f_3(x)\\ f_1'(x) & f_2'(x) & f_3'(x)\\ f_1''(x) & f_2''(x) & f_3''(x) \end{array} \right|$ and the functions are linearly independent if the wronskian is nonzero.