Notation & Linear

[Zhiya Lou]

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)  $u_{𝑥𝑥𝑥𝑥}+2u_{𝑥𝑥𝑦𝑦}+𝑢_{𝑦𝑦𝑦𝑦}=0$

[Kathryn Bucci]

$u_x$ = partial derivative of $u$ with respect to $x$
$u_{xx}$ = second partial derivative of $u$ with respect to $x$

22) is not linear because of the two terms where u is multiplied by $u_x$ and $u_y$

I fixed math expressions for both of you. "Edit" to see how it should be done-V.I.