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3 years ago

In the below system, solve for y in the first equation.

Mathematics

1 answer:

Flura [38]3 years ago

5 0

C
$x - 3y = - 6 \\ - 3y = - 6 - x \\ \frac{ - 3y}{ - 3} = \frac{ - 6 - x}{ - 3} \\ y = 2 - x \\or \\ y = - x + 2$

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Solve these linear equations in the form y=yn+yp with yn=y(0)e^at.

WINSTONCH [101]

Answer:

a) $y(t) = y_{0}e^{4t} + 2$ . It does not have a steady state

b) $y(t) = y_{0}e^{-4t} + 2$ . It has a steady state.

Step-by-step explanation:

a) $y' -4y = -8$

The first step is finding $y_{n}(t)$ . So:

$y' - 4y = 0$

We have to find the eigenvalues of this differential equation, which are the roots of this equation:

$r - 4 = 0$

$r = 4$

So:

$y_{n}(t) = y_{0}e^{4t}$

Since this differential equation has a positive eigenvalue, it does not have a steady state.

Now as for the particular solution.

Since the differential equation is equaled to a constant, the particular solution is going to have the following format:

$y_{p}(t) = C$

$(y_{p})' -4(y_{p}) = -8$

$(C)' - 4C = -8$

C is a constant, so (C)' = 0.

$-4C = -8$

$4C = 8$

$C = 2$

The solution in the form is

$y(t) = y_{n}(t) + y_{p}(t)$

$y(t) = y_{0}e^{4t} + 2$

b) $y' +4y = 8$

The first step is finding $y_{n}(t)$ . So:

$y' + 4y = 0$

We have to find the eigenvalues of this differential equation, which are the roots of this equation:

$r + 4 =$

$r = -4$

So:

$y_{n}(t) = y_{0}e^{-4t}$

Since this differential equation does not have a positive eigenvalue, it has a steady state.

Now as for the particular solution.

Since the differential equation is equaled to a constant, the particular solution is going to have the following format:

$y_{p}(t) = C$

$(y_{p})' +4(y_{p}) = 8$

$(C)' + 4C = 8$

C is a constant, so (C)' = 0.

$4C = 8$

$C = 2$

The solution in the form is

$y(t) = y_{n}(t) + y_{p}(t)$

$y(t) = y_{0}e^{-4t} + 2$

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3 years ago

How come the tutors don't work??

joja [24]

Answer:

What do you mean? If you are talking about the Community not always answering Questions well that means your they don't know the right Answer

the Mods are Annoying and very skeptic of the Guidelines of Brainly.

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3 years ago

Please help ASAP!! Algebra (equation in picture)

BabaBlast [244]

[-8,8] because both points are closed points.

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3 years ago

How to find the other endpoint of a line when only given the first endpoint and the midpoint?

Schach [20]

If we have a line, and the endpoints are(x₁,y₁) and (x₂,y₂), the midpoint will be:( (x₁+x₂)/2 , (y₁+y₂)/2 );

Data:
Endpoint₁: (2,-3)
Midpoint: (6,6)

Therefore:

(2+x₂)/2=6
2+x₂=12
x₂=12-2
x₂=10

(-3+y₂)/2=6
-3+y₂=12
y₂=12+3
y₂=15

Answer; the other endpoint of a line will be (10,15)

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Step-by-step explanation:

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