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14)Show that u(x, y) = 2y + 3x²y-y³ is harmonic and find its conjugate harmonic function v(x, y) and the corresponding analytic function f(z).
Explain the problem with step by step process?
13)Show that the function f (z)=(z̅ )²/z,z≠0 ;0, z=0 satiesfies Cauchy-Rieman equations at z=0.Does f'(0) exist? Explain the problem with step by step process?
12) Find the complete integral of the PDE p²+q²=1
Explain the problem with step by step process?
10)Find the complete integral of the PDE yq+3xp=2(z-y²p²).
Explain the problem with step by step process?
9) Eliminate the arbitrary constants a and b from the equation (x-a)²+(y-b)²+z²=2019 to obtain the partial differential equation.
Explain the problem with step by step process?
8)Solve (D²+3DD'+2D'^2)z=x cos y+e^x+y, Where D=∂\∂x and D'=∂\∂y.
Explain the problem with step by step process?
7)Find the integral surface of x(y²+z)p-y(x²+z)q=(x²-y²)z through the curve x+y=0,z=1.
Explain the problem with step by step process?
5)Solve ∫0^t y''(τ)y'(t-τ)dτ=y(t),y(0)=y'(0)=20
