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MAT244--Lectures & Home Assignments / Wronskian for real equal roots
« on: October 07, 2018, 10:39:37 PM »
For Wronskian determinant, $y_1$ and $y_2$ is the fundamental set of solution if W is not 0 (for all $t$?)
But, if W could be 0 for some t, does the statement still hold?
Particularly in the real equal root example:
$y''$- $2y'$ + $y$ = 0
$y_1$ = $e^t$
$y_2$ = $t$$e^t$
$W = t^2 e^{2t}-t e^{2t} = 0$ if $t=1$ or $0$ WRONG
How to think about this kind of situation? if there is no restriction on $t$
But, if W could be 0 for some t, does the statement still hold?
Particularly in the real equal root example:
$y''$- $2y'$ + $y$ = 0
$y_1$ = $e^t$
$y_2$ = $t$$e^t$
$W = t^2 e^{2t}-t e^{2t} = 0$ if $t=1$ or $0$ WRONG
How to think about this kind of situation? if there is no restriction on $t$