Chemical Engineering Answers

2) Show that v(x,y)=x²-y²-y is harmonic function.Find it's conjugate harmonic function u(x,y) and corresponding analytic function f(z).

1) Is the function f(z)={[Rez-lmz]²/|z|² ,z≠0 ;0 ,z=0 Continuous at z=0?

6)Solve ∂²z/∂x²-∂²z/∂y²=e^{x-2y}+ cos(2x+3y).

5) Find the particular integral of ∂²z/∂x²-3 ∂²z/∂x∂y+∂²z/∂y²= 2x sin y.

4)Find the complete integral of xp+3yq=2(z-x²q²)

3) Find the complete integral of p^3+q^3=27Z.

6) Solve the initial value problem y''-4y=cos 3t ,y(0)=0,y'(0)=1

5)Solve the integral equation f(t)=t+3 ∫0^t f(τ)dτ?

4) Find the inverse Laplace transform of 5/(s-1)(s+4) without using partial fractions.

3) Find the inverse Laplace transform of ln(s+3/s²+9).