Wronskiaan van $$$t$$$, $$$t^{2}$$$
Uw invoer
Bereken de Wronskiaan van $$$\left\{f_{1} = t, f_{2} = t^{2}\right\}$$$.
Oplossing
De Wronskiaan wordt gegeven door de volgende determinant: $$$W{\left(f_{1},f_{2} \right)}\left(t\right) = \left|\begin{array}{cc}f_{1}\left(t\right) & f_{2}\left(t\right)\\f_{1}^{\prime}\left(t\right) & f_{2}^{\prime}\left(t\right)\end{array}\right|.$$$
In ons geval geldt $$$W{\left(f_{1},f_{2} \right)}\left(t\right) = \left|\begin{array}{cc}t & t^{2}\\\left(t\right)^{\prime } & \left(t^{2}\right)^{\prime }\end{array}\right|.$$$
Bepaal de afgeleiden (voor de stappen, zie afgeleiderekenmachine): $$$W{\left(f_{1},f_{2} \right)}\left(t\right) = \left|\begin{array}{cc}t & t^{2}\\1 & 2 t\end{array}\right|$$$.
Bereken de determinant (voor de stappen, zie determinant calculator): $$$\left|\begin{array}{cc}t & t^{2}\\1 & 2 t\end{array}\right| = t^{2}$$$.
Antwoord
De Wronskiaan is gelijk aan $$$t^{2}$$$A.