1. ## Harmonic Functions

show that the function f(x,y)= (x^3)(y)-(x)(y^3) is a harmonic function.

show that the function f(x,y)= (x^3)(y)-(x)(y^3) is a harmonic function.
This is very easy if you use the definition of harmonic function. Just show $f_xx + f_yy = 0$.
You need to compute all those partial derivatives.