The question is:
Examine a differential equation expressed as
y′ = f(αt + βy + γ),
where α, β, and γ are constants. Employ the variable change
z = αt + βy + γ to reformulate the differential equation as a separable equation of the type z′ = g(z).
Answer:
The equation
y′ = f(αt + βy + γ)
can be rephrased as
dy/dt = f(αt + βy + γ).
Our goal is to rewrite this differential equation in the form
z' = g(z), that is dz/dt = g(z).
First, be aware that
dz/dt = (dz/dy) * (dy/dt)...................(1)
Utilizing the substitution
z = αt + βy + γ
as specified,
dz/dy = β..........................................(2)
dy/dt = f(αt + βy + γ) = f(z)............(3)
From equations (2) and (3),
dz/dt = β.f(z) = g(z)
Thus,
z' = g(z)
Where g(z) = βf(z).
Answer: The precise answer is 2/3x + 17
Step-by-step explanation:
Answer:
3l= c
Step-by-step explanation:
This requires using 3 cups of cranberry juice, along with 1 cup of lemonade.
Detailed explanation:
Thus,
100% plus 8% equals 108%
108% equals 1215
1% corresponds to 11.25
Therefore, 100% amounts to 1125 rs
Answer: the independent variable is time (t). The dependent variable is distance (d).
Step-by-step explanation: an independent variable is defined as one whose variation is not dependent on another. In this case, time acts as the independent variable because it continues to pass irrespective of other factors. The distance is considered the dependent variable, as Jillian's distance traveled relies on the duration she spends walking and jogging.
