Put the differential equation 9ty+ety′=yt2+81 into the form y′+p(t)y=g(t) and find p(t) and g(t). p(t)= help (formulas) g(t)= help (formulas) Is the differential equation 9ty+ety′=yt2+81 linear and homogeneous, linear and nonhomogeneous, or nonlinear?

Answers

Answer 1

Answer:

[tex]p(t) = \frac{9t^{3} + 729t - 1}{e^{t}(t^{2} + 81) }[/tex]

g(t) = 0

And

The differential equation [tex]9ty + e^{t}y' = \frac{y}{t^{2} + 81 }[/tex] is  linear and homogeneous

Step-by-step explanation:

Given that,

The differential equation is -

[tex]9ty + e^{t}y' = \frac{y}{t^{2} + 81 }[/tex]

[tex]e^{t}y' + (9t - \frac{1}{t^{2} + 81 } )y = 0\\e^{t}y' + (\frac{9t(t^{2} + 81 ) - 1}{t^{2} + 81 } )y = 0\\e^{t}y' + (\frac{9t^{3} + 729t - 1}{t^{2} + 81 } )y = 0\\y' + [\frac{9t^{3} + 729t - 1}{e^{t}(t^{2} + 81) } ]y = 0[/tex]

By comparing with y′+p(t)y=g(t), we get

[tex]p(t) = \frac{9t^{3} + 729t - 1}{e^{t}(t^{2} + 81) }[/tex]

g(t) = 0

And

The differential equation [tex]9ty + e^{t}y' = \frac{y}{t^{2} + 81 }[/tex] is  linear and homogeneous.


Related Questions

Luis compra 126 celulares a $268 por cada uno. Cada celular fue vendido a $325 ¿Cuánto dinero gano Luis?

Answers

Answer:

Ganancia total= $7.182

Step-by-step explanation:

Dada la siguiente información:

Luis compra 126 celulares a $268 por cada uno. Cada celular fue vendido a $325.

Primero debemos calcular cuanto gana con cada celular:

Ganancia unitaria= 325 - 268

Ganancia unitaria= $57

Ahora, la ganancia total:

Gnanacia total= 57*126

Ganancia total= $7.182

Mhanifa please help! If I don’t get this done I will fail this class :(

Answers

Answer:

#1

x/9 = tan 60°x = 9 tan 60° x = 15.6 m

#2

cos θ = 15.1/16.5cos θ = 0.915θ = arccos (0.915)θ = 23.8°

#3

10/x = tan 42°x = 10 / tan 42°x = 11.1 m

Aircraft A has 126 more seats than aircraft B. If their total number of seats is 440 ​, find the number of seats for each aircraft.

Answers

Answer:

Aircraft A = 283 seats

Aircraft B = 157 seats

Step-by-step explanation:

Aircraft A = B + 126

Aircraft B

A + B= 440

B + 126 + B= 440

Collect the like terms

B+B+126= 440

2B+126= 440

2B= 440-126

2B= 314

B= 157

Substitute 157 for B in equation 1

A= B+126

A= 157+126

A= 283

Hence Aircraft A has 283 seats and Aircraft B has 157 seats

I need help with these too if you help me and graph and tell it how did you get the answer I will give you 20 points.

Answers

Answer:

I only know number 11 sorry :(

11. (Image attached)

Step-by-step explanation:

First, I would find the y intercept, which is 4. Next I found the slope of -3 by finding the rise of -3 (3 to left), then the run (1 up).

---------------------------------------------------------------------------------------------------------------

Have a good day :)

Item 23 Find the sale price. Original price: $50 Discount: 15%

Answers

Answer:

42.50

Step-by-step explanation:

50 x.15 =7.50 discount

50 (original price)-7.50 (discount)=42.50 (sales price)

please please help!! i don’t know how to do this

Answers

Answer:

What is your question I will not see and understand

Which question is a statistical question? A Which U.S. States have mountains?Which U.S. States have mountains? B Which mountain range do U.S. Citizens most enjoy visiting?Which mountain range do U.S. Citizens most enjoy visiting? C How many mountain ranges are in the U.S.?How many mountain ranges are in the U.S.? D How tall is the tallest mountain in the U.S.?

Answers

Answer: C. How many mountain ranges are in the U.S.

Step-by-step explanation:

A statistical question first of all has to have a quantitative response i.e., answers should be in numbers.

The only two questions here that would yield a numeric answer are options C and D.

Furthermore, a statistical question has variability in it which means that the answer is based on multiple observations not just one. The observations in option C are mountain ranges and as the question requires finding out details about multiple mountain ranges, this is a statistical question.

This is opposed to option D which addresses issues surrounding just one mountain.

PLEASE HELP!!! MATH 14.1 The law of sines

Answers

Answer:

[tex]\huge\boxed{Law \ Of \ Sines \hookleftarrow}[/tex]

[tex]\huge\bold{\frac{a}{ \sin (A)} = \frac{b}{ \sin \: (B) } = \frac{c}{ \sin \:( C) }} [/tex]

➟ In a triangle, side “a” divided by the sine of angle A is equal to the side “b” divided by the sine of angle B is equal to the side “c” divided by the sine of angle C.

# ꧁❣ RainbowSalt2²2² ࿐

Answer: Law of Sines


Have a good day

Please help with this, will give brainliest.

Answers

Answer:

Its A y=3

Step-by-step explanation:

Answer:

A- y=3

Step-by-step explanation:

3x+4y=30

3x+5y=33

-3x+-4y=-30

3x+5y=33

-4y=-30

5y=33

y=3

evaluate2x
X= 5 -3
-4 2​

Answers

Answer :

Evaluate

Isolate the variable by dividing each side by factors that don't contain the variable.

x = 2 i √ 5 , − 2 i √ 5

Step-by-step explanation:

The net below represents a container.
What solid figure is represented by the net?

Answers

Answer:

Triangular prism

Step-by-step explanation:

Triangle baces and Rectangle sides make a Triangular prism.

on Monday, there were 18 chickens and 12 sheeps in a field. there were no other animals in the field. what was the ratio of chickens to sheep i the field on monday?


Answers

Answer:

18:12

Step-by-step explanation:

The ratio of chickens to sheep in the field on monday is 2 : 3.

What are ratio and proportion?

In its most basic form, a ratio is a comparison between two comparable quantities.

There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.

If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.

Given, On Monday, there were 18 chickens and 12 sheeps in a field.

Therefore, For every 18 chickens there is 12 sheeps in the feild.

So, Monday's chickens to sheep ratio in the field is,

Chicken : Sheep = 12 : 18.

Chicken : Sheep = 4 : 6.

Chicken : Sheep = 2 : 3.

learn more about proportion here :

https://brainly.com/question/7096655

#SPJ2

A coin is flipped 3 times. What is the probability that it lands on heads exactly 3 times? Write your answer as a reduced fraction (numerator/denominator).

Answers

Answer:

1/3

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

three tries so your demonater is 3, 1 chance so numerator 1

HELP PLEASEEEEEEE
Suppose x = 7 is a solution to the equation 4x – 2(x + a) = 8.
Find the value of a that makes the equation true.
-25
2
3
6

Answers

=> 4(7)–2(7+a)=8

=>28–142a=8=>14–2a=8=>-2a=8–14=>-2a=-6=>a=3

if x+y=12 and xy=27 . find x^3+y^3
pls help with steps ​

Answers

Answer:

Step-by-step explanation:

use formula

x^3+y^3=(x+y)^3-3*x*y(x+y)

=12^3-3*27(12)

=1728-972

=756

Answer:

x^3 + y^3 = 756

Step-by-step explanation:

Given that,  x+y=12 and xy=27

We know that,

[tex]( x + y )^3 = x^3 + y^3 + 3xy(x + y)[/tex]

∴ [tex]12^3 = x^3 + y^3 + 3 * 27 * 12[/tex]

[tex]=> 1728 = x^3 + y^3 + 972[/tex]

[tex]x^3 + y^3 = 1728 - 972[/tex]

[tex]==> x^3 + y^3 = 756[/tex]

What describes a statistical sample?

Answers

Answer:

Statistical sampling is drawing a set of observations randomly from a population distribution. ... By repeating the sampling operation a large number of times, perhaps 1000, we decrease the sampling error and increase the quality of the estimates.

Answer:

Heya Buddy!

Step-by-step explanation:

Statistical sampling is drawing a set of observations randomly from a population distribution. ... By repeating the sampling operation a large number of times, perhaps 1000, we decrease the sampling error and increase the quality of the estimates.

Hope that helps..

Take care..

Bye!

A card is drawn from a five-card hand. The cards are labeled A, B, C, D, F. Then a spinner with 3 sections labeled as 1, 2, 3 is spun. What is the sample space?

Answers

Answer:

The sample space is the set of all the possible outcomes of a given experiment.

Here, our experiment consists on:

Drawing a card from a five-card hand, such that the outcomes there are:

A, B, C, D, E  (5 outcomes)

Followed by spinning a spinner with 3 sections labeled 1, 2 and 3 (3 outcomes).

The total number of outcomes of the combined event, is equal to the product between the numbers of outcomes for each event.

So for our experiment, the total number of outcomes is:

C = 5*3 = 15 outcomes.

And these outcomes are like:

Drawing the card A and spinning a 1 (represented with A-1)

Drawing the card C and spinning a 2 (represented with C-2)

etc.

The set of all possible outcomes are:

{A-1, A-2, A-3, B-1, B-2, B-3, C-1, C-2, C-3, D-1, D-2, D-3, F-1, F-2, F-3}

Find the roots of the Equation 16+x^2=0

Answers

Answer:

x = 0   or   x = - 16

Step-by-step explanation:

16+x^2=0

x ( x + 16 ) = 0

using the algebra rule a . b = a = 0 and b = 0

x = 0    or   x = - 16

so the answer is  x = 0 and x = -1 6

Mark brainliest plsssssssssss

HIE
YA
HHHHHHHH111111111111
Use the calculator to fill
in the table & graph for
the equation y=3x - 2.
6
5
у
3
2
1
1 2 3 4 5 6
0
-6-5-4-3-2-1
-11
-2-
-3
1
2
-5
-6
3
Students, draw anywhere on this slide!

Answers

Answer:

y = 3x-2

Step-by-step explanation:

which expression is equivalent to 4+x+x+2x+5+3+x?
A.17x
B.5x+14
C.4x+14
D.2x+15x

Answers

the answer is b 5x+14

[tex]\boxed{B.\:5x\:+\:12}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]4 + x + x + 2x + 5 + 3 + x \\ = (x + x + 2x + x) + 12 \\ since \: they \: are \: like \: terms, \: we \: can \: add \: them \\ = 5x + 12[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]

Help, please!! I don’t have much time

Answers

Answer:

B.

Step-by-step explanation:

PLEASE HELP ME !! I NEED TO PASS !!

Answers

Answer:

216 ft squared

Step-by-step explanation:

[tex]18*12=216ft^{2}[/tex]

216 feet squared / C

Represent root 2 on the number line

Answers

Look at the both picture.


Find the value of x in the figure.
570
(x+23)°
x =

Answers

Answer:

Step-by-step explanation:

Assuming you meant

570=(x+23)

570-23=x

547 = x

ASAP
-WILL MARK BRIANIST
thank you <3

Answers

Answer:

d

Step-by-step explanation:

D
12-x
12 less than x which than equals whatever number

A line, line segment, or ray that intersects a line segment at its midpoint is a segment bisector. True or fals?

Answers

Answer:

true.

Step-by-step explanation:

hope this helps, i looked it up :)

True
Because I did this already and got right

Round 1.3185 to 1 decimal place

Answers

Answer:

1

Step-by-step explanation:

Because 1.38185 is below 1.5 so it rounds to 1

the answer to the question is 1

Write the equation of the line in fully simplified slope-intercept form

Answers

The equation of the line is y=-x+2

(NR) Natural Resources:Question 10
Which statement best describes why large aquifers of groundwater are distributed unevenly
around the earth?

Answers

Answer: D) Groundwater collects only where the soil and geological features allow water to seep down into underground chambers.

In other words, as long as there are gaps to allow water through, then that would lead to underground aquifers. Another important component is the amount of rain water that happens. Sources such as rivers, lakes and streams are also a contributing factor.

Stuff like earthquakes, volcanic activity, and continental movement doesn't really have much an effect on where or how aquifers form. It's really all about the soil type and how the landscape is formed, and of course the other factors mentioned in the previous paragraph.

how to solve 6x - 9 - 2 (1 - x) = x + 9​

Answers

[tex]x = 2.857[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]6x - 9 - 2(1 - x) = x + 9 \\ ⇢ 6x - 9 - 2 + 2x = x + 9 \\ ⇢ 8x - x = 9 + 11 \\ ⇢ 7x = 20 \\ ⇢  x = \frac{20}{7} \\ ⇢ x = 2.857[/tex]

[tex]{ \bf{ \underbrace{To\:verify:}}}[/tex]

[tex]6 \times 2.857 - 9 - 2(1 - 2.857) = 2.857 + 9 \\ ➪ \: 17.142 - 9 - 2 \times( - 1.857) = 11.857 \\➪ \: 8.142 + 3.714 = 11.857 \\➪ \: 11.856 = 11.857 \\ ➪ \: 11.86 = 11.86 \\ ➪ L.H.S.=R. H. S [/tex]

Hence verified.

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]

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