Answer
The Laplace's equation is satisfied.
Work Step by Step
We need to verify the Laplace's equation $\nabla^2 f =\dfrac{\partial^2 f}{\partial x^2}+\dfrac{\partial^2 f}{\partial y^2}=0$
We take the first partial derivative of the given function $f(x,y)$ with respect to $x$, by treating $y$ as a constant, and vice versa:
$f_x=3 \\ f_y=2$
Now we take the second order partial derivatives:
and $f_{xx}=0 \\f_{yy}=0$
Now, $\nabla^2 f =0+0=0$
So, the Laplace's equation is satisfied.