Question

a)Prove that the function u(x, y) = x -y÷x+y is harmonic and obtain a conjugate function...

a)Prove that the function
u(x, y) = x -y÷x+y
is harmonic and obtain a conjugate function v(x, y) such that
f(z) = u + iv is analytic.

b)Convert the integral
from 0 to 5 of (25-t²)^3/2 dt
into a Beta Function and evaluate the resulting function.

c)Solve the first order PDE
sin(x) sin(y)
∂u
∂x + cos(x) cos(y)
∂u
∂y = 0
such that u(x, y) = cos(2x), on x + y =
π
2

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