Answer Happy

11. A function of two variables u(x, y) is said to be harmonic on a domain D if it satisfies the equation Uxx + Uyy = 0 throughout D. Show that the following functions are harmonic by checking the above definition: (a) x² − 6x²y² + y² 1 log(x² + y²) where (x, y) ‡ (0,0). (b)