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
Answer:
(y equals start fraction two over three end fraction x)
Step-by-step explanation:
Lest's organize the table values of our function first:
x y
-6 -4
-3 -2
0 0
3 2
The simplest kind of of function is a linear function of the form where
is the slope and
is the y-intercept. Let's us check if our function is a linear one finding its equation and checking that all points are in the line.
The first step to find a linear equation is find the slope of the line; to do it, we are using the slope formula:
where
is the slope of the line
are the coordinates of the first point
are the coordinates of the second point
We know from our table that the first and second points are (-6, -4) and (-3, -2) respectively, so ,
,
, and
.
Replacing values:
Now that we have the slope of our line we can use the point slope formula to complete our linear function:
where
is the slope
are the coordinates of the first point
Replacing values:
Now, to check if our function is valid, we can either check if each point satisfies the rule , or we can graph it and check if each lies is in the graph.
Let's check both:
We already know that points (-6, -4) and (-3, -2) satisfy the rule (after all, those were the point we used to came out with the rule in the first place), so we just need to check the points (0, 0) and (3, 2)
- For (0, 0):
The point satisfies the rule.
- For (3, 2):
The point satisfies the rule.
Since all the points of our table satisfies the rule , we can conclude that the rule describing the function shown is
.
