Wronskian
WronskianΒΆ
\[
\begin{gather}
W(y_1, y_2, \dots , y_n) = det
\begin{bmatrix}
y_1 & y_2 & \dots & y_n\\
y_1' & y_2' & \dots & y_n'\\
\vdots & \vdots & \ddots & \vdots\\
y_1^{(n-1)} & y_2^{(n-1)} & \dots & y_n^{(n-1)}
\end{bmatrix}
\end{gather}
\]
\[W \neq 0 \qquad \rightarrow \qquad \text{linearly independent}\]