b=3
I found this out by subtracting and adding on both sides.
The same line is written in two different forms
Answer:
Linear and non-homogeneous.
Step-by-step explanation:
We are given that

We have to convert into y'+P(x)y=g(x) and determine P(x) and g(x).
We have also find type of differential equation.



It is linear differential equation because this equation is of the form
y'+P(x)y=g(x)
Compare it with first order first degree linear differential equation



Homogeneous equation

Degree of f and g are same.

Degree of f and g are not same .
Therefore, it is non- homogeneous .
Linear and non-homogeneous.
9514 1404 393
Answer:
y = (5/27)(x -7)^2 -5/3
Step-by-step explanation:
Use the given points to find the unknowns in the equation.
If the axis of symmetry is x=7, then the equation can be written in the form ...
y = a(x -7)^2 +b
Filling in the two point values, we have two equations:
0 = a(4 -7)^2 +b ⇒ 9a +b = 0
5 = a(1 -7)^2 +b ⇒ 36a +b = 5
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Subtracting the first equation from the second, we have ...
(36a +b) -(9a +b) = (5) -(0)
27a = 5
a = 5/27
Substituting that value into the first equation gives ...
9(5/27) +b = 0
5/3 +b = 0
b = -5/3
So, the quadratic can be written in vertex form as ...
y = (5/27)(x -7)^2 -5/3