Question

(a) Let f(x,y) = axy + ax^2y + y^3. Find div(gradf).
div(gradf) =



(b) Find a value of a so that div(gradf) = 0 for all x, y.
a =

Answer 1

The gradient is\[
\left(2 a x y+a y,a x^2+a x+3 y^2\right)\]
What is its divergence?

Answer 2

Its divergence is
\[
6y + 2 a y= 2y(3 + a)
\]

Answer 3

It is enough to take a=-3

Answer 4

thank you so much