Wronskian dari $$$x$$$, $$$x^{5}$$$

Hitung Wronskian dari $$$\left\{f_{1} = x, f_{2} = x^{5}\right\}$$$.

Wronskian diberikan oleh determinan berikut: $$$W{\left(f_{1},f_{2} \right)}\left(x\right) = \left|\begin{array}{cc}f_{1}\left(x\right) & f_{2}\left(x\right)\\f_{1}^{\prime}\left(x\right) & f_{2}^{\prime}\left(x\right)\end{array}\right|.$$$

Dalam kasus ini, $$$W{\left(f_{1},f_{2} \right)}\left(x\right) = \left|\begin{array}{cc}x & x^{5}\\\left(x\right)^{\prime } & \left(x^{5}\right)^{\prime }\end{array}\right|.$$$

Temukan turunan (untuk langkah-langkahnya, lihat kalkulator turunan): $$$W{\left(f_{1},f_{2} \right)}\left(x\right) = \left|\begin{array}{cc}x & x^{5}\\1 & 5 x^{4}\end{array}\right|$$$

Temukan determinan (untuk langkah-langkah, lihat kalkulator determinan): $$$\left|\begin{array}{cc}x & x^{5}\\1 & 5 x^{4}\end{array}\right| = 4 x^{5}$$$

Wronskian sama dengan $$$4 x^{5}$$$A.