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Topics - Zhiya Lou

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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 $t$

MAT244--Lectures & Home Assignments / Notation & Linear
« on: September 16, 2018, 08:36:44 PM »
HI, I don't understand the notation from these question (sec1.3); And also about its linear/non-linear property... Thanks
22) $𝑢_{𝑥𝑥}+u_{𝑦𝑦}+𝑢𝑢_𝑥+𝑢𝑢_𝑦+u=0$

(why is it non linear?)

23)  $u_{𝑥𝑥𝑥𝑥}+2u_{𝑥𝑥𝑦𝑦}+𝑢_{𝑦𝑦𝑦𝑦}=0$

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