Calculus

Which of the following functions satisfy the two-dimensional Laplace equation $\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0$?

Options:

• (A) $u(x, y) = x^2 - y^2$
• (B) $u(x, y) = e^x \cos y$
• (C) $u(x, y) = \ln(x^2 + y^2)$ for $(x,y) \neq (0,0)$
• (D) $u(x, y) = x^2 + y^2$