Solve the following IVPs using Laplace transform: a. y' + 2y' + y = 0, y(0) = 2, y'(0) = 2.

Answers

Answer 1

The solution to the IVP is:

y(t) = 4e^(-t), y(0) = 2, y'(0) = 2.

To solve this IVP using Laplace transform, we first take the Laplace transform of both sides of the differential equation:

L{y' + 2y' + y} = L{0}

Using the linearity of the Laplace transform and the derivative property, we can simplify this to:

L{y'} + 2L{y} + L{y} = 0

Next, we use the Laplace transform of the derivative of y and simplify:

sY(s) - y(0) + 2sY(s) - y'(0) + Y(s) = 0

Substituting in the initial conditions y(0) = 2 and y'(0) = 2, we have:

sY(s) - 2 + 2sY(s) - 2 + Y(s) = 0

Simplifying this equation, we get:

(s + 1)Y(s) = 4

Dividing both sides by (s + 1), we get:

Y(s) = 4/(s + 1)

Now, we need to take the inverse Laplace transform to get the solution y(t):

y(t) = L^-1{4/(s + 1)}

Using the Laplace transform table, we know that L^-1{1/(s + a)} = e^(-at). Therefore,

y(t) = L^-1{4/(s + 1)} = 4e^(-t)

So the solution to the IVP is:

y(t) = 4e^(-t), y(0) = 2, y'(0) = 2.

Learn more about IVP here:

https://brainly.com/question/23864530

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Related Questions

y = 3x + 6
y = (x + 4)2 – 10

What’s the solution set for this

Answers

The answer is,

y = -18, x = -8

−4p+9=−5


Plzzzzzzz help

Answers

Answer:

p = 3.5 or p = 7/2

Step-by-step explanation:

-4p+9= -5

or, -4p = - 14

or, p = -14/-4

or, p = 7/2 = 3.5

Answer:

p = 3.5

Step-by-step explanation:

What you would do to get p is subtract 5 from both sides of the equation to leave the number and p, THEN divide both sides by the numerator of -4.

-4p + 9 = -5

      - 9     -9

__________

-4p = -14

__      __

-4         -4

Thus, p = 3.5

6x+8> −16 please help

Answers

Answer:

 x = 4

Step-by-step explanation:

I hope this helps sorry if its wrong

Simplify the following
√2+√3/3√2-2√3​

Answers

Answer:

a

Step-by-step explanation:

plzzzzzzzzzzzzz help

Answers

Answer:

[tex]5*\frac{1}{2}[/tex]

Step-by-step explanation:

We have a picture and are being asked to identify the multiplication problem that represents it.

So we have 5 triangles, all of which are color-coded in red, but only half of them are filled. When multiplying, the number that is before the * sign is the amount there is, while the number that is after the * is the amount going to multiply the amount of items there are. So looking at the picture, we can see 5 triangles, therefore :

5 *

2 * 1/5 is scratched out as an answer. As is starts with 2.

As for the second number, we acknowledge that all triangles are half in red, therefore the number is 1/2.

5 * 1/2

Scratching all other answers.

Bethany uses the equation d = 4.25h to find the distance, d, she travels while walking for h number of hours. What is the constant of proportionality between d and h?

Answers

Answer:

4.25

Step-by-step explanation:

The distance Bethany travels is directly proportional to the number of hours she spends working

The formula for direct proportion is :

y = kx

Where k is a constant

in this question, the constant is given by 4.25

ans of this question
4 (3c+4d)

Answers

Answer: 12c+16d

Step-by-step explanation: 4(3c+4d)

(4)(3c+4d)

(4)(3c)+(4)(4d)

12c+16d

Answer:

Întâi faci paranteza și după de ie faci cu 4

Michael mowed lawns during the summer to earn extra money. He charged each customer $30 to cut the grass plus $9 for each hour of work. One customer paid Michael $93. How long did it take Michael to mow that customer's lawn?

Answers

Answer: 7 hours


Explanation: We can use the equation 93=9h+30 to represent the problem.

When we solve for h with (93-30)/9, we get 7 hours.

\angle a∠aangle, a and \angle b∠bangle, b are complementary angles. \angle a∠aangle, a measures 59^\circ59

59, degrees.
What is the measure of \angle b∠bangle, b?

Answers

Answer:

31°

Step-by-step explanation:

because angle a and angle b are complementary they equal 90 degrees in total

a+b=90

since angle a = 59°

59+b=90

so you use subtraction property of equality and subtract 59 from both side of the equal sign

59+b=90

-59    -59

b= 31°

PLEASE HELP WILL GIVE BRAINLY its down below

Answers

Answer:

A.) $383 500 000/year

B.) $826 750 000/year

Step-by-step explanation:

Just add the number of sales and divide to how many year of sales it was and you will get the answer.

A two digits number is 21 times the difference and 350% of the product of its digit. Find the quotient of the digit of number​

Answers

The number is 63, so the quotient is 2.

Two digit numbers divisible by 21:
21, 42, 63, 84

21: 2-1 = 1 * 3.5 = 3.5
3.5*2*1 = 7 but 7 does not equal 21

42: 4-2 = 2 * 3.5 = 7
3.5*4*2 = 28 does not equal 42

63: 6-3 = 3*3.5 = 13.5
3.5*6*3 = 63 :)

Check:
21(6-3)=21(3)= 63 :)
3.5(6)(3) = 21(3) = 63 :)

63: 6/3 = 2

Daniel used to collect baseball cards as a kid. He purchased a particular
card for $30 in 2006 and the value of the card increases by 2.5% per year.
How much is his card worth now (in 2021)? Use units and round
appropriately.

Answers

Answer:

[tex]y < 85 \div \div 9614 = 88[/tex]

Ты лоххх

PLZ HELP ME I NEED HELP ASAP

Answers

Answer:

75 I hope this helped and brainliest please!

Step-by-step explanation:

The equation for surface area for a square pyramid is A=a squared + 2a times the square root of (a squared over 4) + height squared. Since everything is 5 yd, the answer is 75.

SOMEONE ANSWER THESE ASAP

MARKING BRAINLIEST

PLEASE HELPPPPP

Answers

Sorry this took a while; calculated a lot of things.

Step-by-step explanation:

A.

Combined:

2.67 times 23.76 = 63.4392

2.67 times - 21 and 5/6 = -58.295

63.4392 - 31.85 -58.295 = -26.7058

If you mean do both separate:

63.4392 - 31.85 = 31.5892

-58.295 - 31.85 = -90.145

B.

Combined:

11 and 3/4 times 23.76 = 279.18

11 and 3/4 times 21 and 5/6 = 256.541666667

279.18 + 256.541666667 + 56 and 3/8 = 592.096666667

If you mean do both separate:

279.18 + 56 and 3/8 = 335.555

256.541666667 + 56 and 3/8 = 312.916666667

Write an expression for the perimeter of the triangle shown below:

Answers

Answer:

7.8x - 17

Step-by-step explanation:

1.8x - 7 + 1.8x - 7 + 3.4x - 3 now add like terms

(variables + variables and Coefficient + Coefficient) so the answer is

7.8x - 17

2 is what percent of 40?

Answers

2 is 5% of 40

Hope it is useful

Petrol is poured into a barrel.
The graph shows the number of litres of petrol in the barrel.
Calculate how much petrol is being poured into the barrel each minute.

Answers

“How much petrol is being poured each minute” is another way of saying slope. Slope is liters/minute, or rise over run.

It rises 140, and goes over 10.

140/10

= 14 liters per minute,

AKAJAXOSPAPXODAOAPA HELP

Answers

Answer:

He used 6 bananas at .50 which cost $3.00

12 oranges at .75 which cost $9.00 and

3 papayas at $1.25 which cost $3.75

Step-by-step explanation:

We can set up a system of equations using the information given.

b for banana, r for orange, p for papaya

b + r + p = 21. Also given r = 2b So substitute to simplify for calculating two unknowns:

b + 2b + p = 21 The number of items.

50b + 75(2b) +125p = 1575 The cost.

I multiplied everything by 100 to eliminate the decimals.

To solve by substituion, rewrite the first equation to get a value for p in terms of b

p = 21 - 3b

Substitute this value in the second equation and solve for b.

50b + 150b + 125(21–3b) = 1575

200b +2625 –375b = 1575 Subtract 2625 from both sides and combine the like terms:

–175b = 1575 –2625

–175b = –1050. Divide both sides by –175

b = 6

Substitute in the original equation to find the amount of each fruit:

b + r + p = 21

b = 6 bananas

r = 2b. 2(6) = 12 oranges. I used r so as not to mix up o with 0.

6 + 12 + p = 21

p = 21 –18

p = 3 papayas

y= 2/3 x +7
X= -4
please help me asap!

Answers

If you’re looking for the x and y intercept them y= 13/3 and x= -4

To get from home to his friend Clayton's house, Eric would have to walk 4 miles due north. To get from home to his friend Dale's house, Eric would have to walk 3 miles due east. What is the straight-line distance between Clayton's house and Dale's house?

PLEASE ANSWER!

Answers

Answer: 5 miles

Step-by-step explanation:

It's a triangle so if you use the pythagorean theorem your equations should look like this. Sqroot of 4^2+3^2 which equals 5. Hope this helps. :)

if hector completed 120 questions last week and 144 this week, how much did he increase by?

Answers

Answer:

he increased by 24

Step-by-step explanation:

144-120

The length of a swimming pool would be about
А
3 feet
12 inches
12 yards
D
3 miles

Answers

It would be 12 yards :)

A small plane flying from Los Angeles to San Diego averaged 175 mph with a tailwind. On the return trip with headwind the average speed was only 125 mph. Write and solve a system to reflect this relationship. Find the speed of the headwind/ tailwind AND the speed of the plane on a calm day.

Answers

Answer:  System of equations:

p + w = 175

p - w = 125

p is the plane's speed, w is the wind speed

The wind speed is 25 mph.  The plane's speed on a calm day is 150 mph.

Step-by-step explanation:

Solve by elimination: Add the equations. w "cancels" solve for p:

p + w = 175

p - w = 125

2p  = 300   divide both sides by 2

p = 150  the plane's speed

Substitute 150 for p and solve for w

150 + w = 175   Subtract 150 from both sides.

w = 25  the wind speed

help help help help help help ill give brainiest

Answers

Answer:

wowee,,, i hope these are right :,)

Step-by-step explanation:

5/3-x+1/3 : -3/2+2+1/2x

3/5-13/5 = 6.9+4.9

3x+0 = 3x

2x-3 = x-3+x

2x-6 = -6+2x

I need help plz and thank you

Answers

Answer:

10

30

18

Step-by-step explanation:

5 tickets is $10
15 tickets is $30
9 tickets is $18

What is the percentage of sugar in the syrup made of 10kg of water and 5kg of sugar? Hi and have a good day :D

Answers

Answer:

33.33%

Step-by-step explanation:

the syrup has a total of 15kg of ingredients, 5kg of it is sugar, so 15/5 which will end as 33.33%

Answer:

33.33%

Step-by-step explanation:

the syrup has a total of 15kg of ingredients, 5kg of it is sugar, so 15/5 which will end as 33.33%

Jared made 12 3 fourhs cups of snack mix for a party his guests ate two thirds of the mix how much snack mix did his guests eat

Answers

Answer: Jared guests ate = 8 1/2 cups of the snack mix.

Step-by-step explanation:

Total snack mix made by Jared = 12 3/4  CUPS

Amount eaten  by guests = 2/3 of Total snack mix

which means they ate = 2/ 3 x12 3/4

= 2/3 x  51/ 4

=17/2 = 8 1/2  cups of snack mix.

Jared guests ate  8 1/2 cups of the snack mix.

In Exercises 13 and 14, find m_1, 22, and m23.
13.
14.
50°
3
1
3 115°
2 1
2

PLEASE HELP

Answers

Answer:

For Question 13 : 1 = 130°; 2 = 50° 3 = 130°

For Question 14 : 1 = 65°; 2 = 115° 3 = 65°

Step-by-step explanation:

Question 13:

There is multiple ways to solve those questions. However I will stick with the simple way.

1) We know that a straighteangle is = to 180°

2) Acording to the statment on step one we will say that 1 + the 50° = 180°

Resoectivelly

180° - 50° = 1

180° - 50° = 130°

1 = 130°

3) 2 + 1 = 180°

We already 1 from step 2, then

2 = 180° - 130°(1)

2 = 50°

4) 2 + 3 = 180°

3 = 180° -  50° ( 2)

3 = 130°

Question 14 1) We know that a straighteangle is = to 180°

2) Acording to the statment on step one we will say that

angle 1 + the angle  115° = 180°

Resopectivelly

180° - 115° = 1

180° - 50° = 65°

1 = 65°

3) 2 + 1 = 180°

We already 1 from step 2, then

2 = 180° - 65°(1)

2 = 115°

4) 2 + 3 = 180°

3 = 180° -  115° ( 2)

Have fun

a number h is at most 15

Answers

hope this is the inequality you’re looking for

Answer:

h inequality 15

hope it is helpful to you

A nesting box for a falcon is put on top of a 96 ft pole. There are 3 ft in 1 yd.

Answers

Answer:

32 yards

Step-by-step explanation:

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