Use the method of laplace transforms to solve the initial value problem: y" -3y'-10y= 0; y(0) =-3, y' (0) 27

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8