Chemical Engineering Answers

8)Show that u(x, y) = 4y + 3x²y-y³ is harmonic and find its conjugate harmonic function v(x, y).

7) Show that the function f(z)={(z̅ )^2,Z≠0. ; 0,Z=0 satisfies Cauchy-Rieman equations at z=0.Does f'(0) exists?

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

Find the complete integral of the PDE px+qy+z=xq²

Find the Laplace transform of the periodic function f(t)=t ,0≤t<1 ; 2-t,1≤t≤2 and f(t+2)=f(t)?

Solve y"+3y'+2y=1, y(0)=0,y'(0)=1.

5)Solve y^2p -xyq = x(z-2y).

4)Find the complete integral of the PDE px + qy +z = xq^2?

Solve y" + 3y' +2y =1, y(0)=0,y'(0) = 1

Find the inverse Laplace transform of In s+3/s^2+9