Question

show that the function satisfies laplace equation
$z = {x}^{2} + {y}^{2}$


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Answer 1

Answer:

0

1

This is a question from my first class on multivariable calculus, where we learned partial derivatives.

given u(x)=ln((x−x0)2+(y−y0)2−−−−−−−−−−−−−−−−−√)

show that u satisfies the laplace equation

∂2u∂x2+∂2u∂y2=0

I have tried to compute these partial derivatives and have seen that subbing in values can produce 0 but computationally somehow fail to do so. I tried it by hand and got the same answer as in maple. In Maple, I got this using x0=a and y0=b

2(x−a)2+(y−b)2−12(2x−2a)2((x−a)2+(y−b)2)2+12(2y−2b)2((x−a)2+(y−b)2)2

but I have no reason to understand why this is equal to zero. Maybe I am manipulating them wrong algabreically or something... could anyone explain how its satisfied?

Step-by-step explanation: