Real Analysis Answers

Find Laplace transform X(p) for function (show all work) in differential equation:
x''''(t)-5x'''(t)-4x''(t)+2x'(t)-x(t)+8=0
x(0)=5
x'(0)-0
x''(0)=-1
x'''(0)=2

Find Laplace transform F(p) for function (show all work)
f(t)=exp(-at)sh(wt)

Find Laplace transform F(p) for function (show all work)
f(t)=sin[(a+ib)t]

let S be a non-empty bounded set in real numbers a) let a>0 , and let aS:={as; s belongs to S} prove that inf(aS)=a inf S, sup(aS)= a sup S

prove by mathematical induction that 2 times 34^n - 3 times 23^n + 1 is divisible by 726 for all positive integers n.

You want to arrange 18 blocks into a rectangular shape. What are all the ways this can be done? (outline the rectangles to illustrate.) Also, What mathematical concept does the first part illustrate?

polynomial f(x)= x4-2x3+3x2-ax+b when divided by (x-1) and (x+1) leaves reminder 5 and 19.Find the values of A and B and the reminder when f(x) is divided by (x-2)

Dear expert give an example of direct and inverse variation in real world.

Find the derivatives of each of the following, showing the working and simplifying.
y = y(x), where x3 sin y + cos(2x + 5y) = 1

Dear Expert sir please give me example of constant in the real world?