Let y′′′−9y′′+20y′=0. find all values of r such that y=erx satisfies the differential equation. if there is more than one correct answer, enter your answers as a comma separated list.

we are given

differential equation as

we are given

Firstly, we will find y' , y'' and y'''

those are first , second and third derivative

First derivative is

Second derivative is

Third derivative is

now, we can plug these values into differential equation

and we get

now, we can factor out common terms

we can move that term on right side

now, we can factor out

now, we can set them equal

so, we will get

...............Answer

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)

it will cost dollar $540

the living room is 3 which means if we divide 325/3 then we get $108

therefore if 1part of the living room cost $108 and 3 costed $325

then total 5part of the room will cost 5*108 which gives $540