Chemical Engineering Answers

15)Find the constants a and b such that the function f (z)=ax-3y+i(bx-2y) is analytic?

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).

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?

12) Find the complete integral of the PDE p²+q²=1

11)Solve the PDE (x+y²)p+yq=z+x².

10)Find the complete integral of the PDE yq+3xp=2(z-y²p²).

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.

8)Solve (D²+3DD'+2D'^2)z=x cos y+e^x+y, Where D=∂\∂x and D'=∂\∂y.

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.

6)If L{f(t)}= e^{-2s}+4/s(2s²+3s+5), then find lim t→∞ f(t)