Find the Laplace Transform of the function F(t) = (1 – e^(-at))/a. Prove by the method of contour integration that F(t) is itself the Laplace Transform of the function arrived at.

Laplace Transform Application of Complex Inversion Integral Formula (Bromwich’s Integral Formula) Problem:- Find the Laplace Transform of the function F(t) = (1 – e^( ...continues

It is a method for finding the integral of some functions by using Laplace Transform. To find the value of ∫ e^(-x^2)dx by using Laplace Transform.

Laplace Transform Inverse Laplace Transform To find the value of ∫ e^(-x^2)dx by using Laplace Transform, where the range of integratio ...continues

Future value

Assume $1000 investment at 10%, for 2 years. What would the fV be?

Grid problem

Five children live in the town of Gridley which is represented by a grid of streets. On the x axis are the streets A, B and so on until Q. On the Y axis, the streets go from descending order from 15th Avenue down to 1st Avenue (in other words as you go up the Y axis, the avenues go down). So at the origin would be the interse ...continues

investigation (Diagonals in a Rectangle)

Diagonals in a Rectangle. In the case of a 2 X 2 rectangle, or a 3 X 5 rectangle, we can simply count. However, can we make a decision about a 100 X 167 or a 3600 X 288 rectangle? In general, given an N X K rectangle, how many grid squares are crossed by its diagonal?

Calculus

Find the order of the differential equation and determine whether it is linear or nonlinear: y^(4) + 3(cos x)y''' + y'=0

Initial value

Solve the initial value problem; it is not necessary to find all solutions of the equation: xy'=y(y-2), y(3)=2

Calculus 3 and 4

Show all work. Please DON'T submit answers back to me as an attachment. Thank you. Determine whether the function is homogenous. If it is, state the degree: f(x, y)=5x^2 + 2xy

Separable/homogeneous

State if the equation is separable or homogeneous: (x^2 + y^2) (dy/dx) = 5xy

Separable/homogeneous

State if the equation is separable or homogeneous: 2xy(dy/dx)=3