Tagged Questions
1
vote
2answers
174 views
How do I show the Wronskian of $(J_{a}(x),Y_{a}(x)) = \dfrac {2} {\pi x}$
Based of using my undergrad class notes. I know that the wronskian of $(J_{a}(x),Y_{a}(x))$ is
$ W(J_{a}(x),Y_{a}(x)) = \left|
\begin{matrix}
J_{a}(x) & Y_{a}(x) \\
J_{a}'(x) & ...
3
votes
1answer
73 views
Characteristic equation for 2-nd order ODE
Given a differential equation $\dot x = Ax$, $x \in \mathbb{R}^n$ we define its characteristic equation as $\chi(\lambda) = \det (\lambda I - A)$. Consider now the second order ODE
$$
\ddot x + A x ...
5
votes
2answers
155 views
Determinant called Grammian
Famously, if functions $f_1,f_2,…,f_n$, each of which possesses a derivative of order $n-1$, are linearly independent on the interval $I$, if
$$ \det\left( \begin{array}{ccccc} f_1 & f_2 & ...
