Consider the initial value problem y′+2y=4t, y(0)=8.

a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s).
b. Solve your equation for Y(s).
c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t).

Please read the complete procedure below:

Step-by-step explanation:

You have the following initial value problem:

a) The algebraic equation obtain by using the Laplace transform is:

next, you replace (1) and (2):

 (this is the algebraic equation)

b)

(this is the solution for Y(s))

c)

To find the inverse Laplace transform of the first term you use partial fractions:

Thus, you have:

(this is the solution to the differential equation)

a function could be identified in 3 ways either on a chart,graph, or ordered pairs. first a function is that each point has its own. the rule is that there can be many x's to one y but there can not be 2 x's at different y's. so on a graph when you put a straight line through the y's there should be one dot only to be a function.

step-by-step explanation:

x> 6

step-by-step explanation:

8x+8> 7x+14

8x-7x> 14-8

x> 6