Engineering Answers

2)Solve y" + 3y' +2y= t²δ(t-2),y(0)=0,y'(0) =-2

1)Find the inverse Laplace transform of ∫s^∞ ln (u+2/u²+9)du.

12)Use Cauchy integral formula for derivatives evaluate ∮c z²-2z/(z+1)^2 (z²+4)dz, where C is |z + 2) <2.

11)Evaluate∫C Im(Z)dz, where C is z = {(t-2i, 1≤t≤2. ; 2-i(4-t), 2<t≤3

11)Evaluate∫C Im(Z)dz, where C is z = {(t-2i, 1≤t≤2. ; 2-i(4-t), 2<t≤3'

10)Using Residue theorem evaluate ∮c Z cosh πz/Z^(4)+5Z^(2)+4, where C is |z| = 3.

9)Find Laurent series expansion of the function 1/ z²+z-6 in the regions

1<|z-1 <4 and |z-1|> 4.

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.