Question

Show that
the function
is harmonic and also
find its harmonic conjugate
x/x2+y2​

Answer 1

Answer:

Evaluate integral of x/(x^2+y^2) with respect to y

∫xx2+y2dy∫xx2+y2dy

Since xx is constant with respect to yy, move xx out of the integral.

x∫1x2+y2dyx∫1x2+y2dy

The integral of 1x2+y21x2+y2 with respect to yy is 1xarctan(yx)+C1xarctan(yx)+C.

x(1xarctan(yx)+C)x(1xarctan(yx)+C)

Simplify the answer.

arctan(yx)+Carctan(yx)+C

Answer 2

Answer:

I don't know??????????