Find the particular solution of the differential equation that satisfies the initial condition(s). f?''(x) = sin(x), f?'(0) = 2, f(0) = 3
f(x)=

Answers

Answer 1

The particular solution of the differential equation is:
f(x) = -sin(x) + 3x + 3

To find the particular solution of the differential equation f''(x) = sin(x) that satisfies the initial conditions f'(0) = 2 and f(0) = 3, follow these steps:

1. Integrate f''(x) = sin(x) once with respect to x:
f'(x) = ∫sin(x) dx = -cos(x) + C₁

2. Use the initial condition f'(0) = 2 to find C₁:
2 = -cos(0) + C₁
C₁ = 3


So, f'(x) = -cos(x) + 3

3. Integrate f'(x) again with respect to x:
f(x) = ∫(-cos(x) + 3) dx = -sin(x) + 3x + C₂

4. Use the initial condition f(0) = 3 to find C₂:
3 = -sin(0) + 3(0) + C₂
C₂ = 3

So, the particular solution of the differential equation is:
f(x) = -sin(x) + 3x + 3

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Related Questions

Please help ❤️❤️❤️❤️❤️❤️❤️

Answers

Answer:

-3/7

Step-by-step explanation:

find two lattice points

the ones I found are (-3, 3) and (4, 0)

use the slope formula

(0-3)/(4-(-3)) = -3/7

josh has 1/4 gallon of orange juice he wants to share it equally between to friends and himself. how much orange juice will each person drink? a 1/12 b 1/8 c 1/3 d 3/4​

Answers

Answer:

a

Step-by-step explanation:

1/4 divided by 3 = 1/(4*3) = 1/12

State whether the triangles are similiar if so write a similarly statement for brainliest

Answers

Answer:

Step-by-step explanation:

The triangles are not similar.

The Triangles are not similar

2x-2
Given f(x) = (2x-2) / 4 solve for f-1(3).

1) 1

2) 5

3) 7

4) 8

Answers

Answer:

Your Streak is on! Answer another question tomorrow and keep it going.

Step-by-step explanation:

help please I really need it

Answers

Answer:

If x is 6, y is 9

Step-by-step explanation:

In your equation, substitute 6 in for each x. This would be (6) + 3y = 4(6) + y.

This ends up being 6 + 3y = 24 + y.

After that, you can subtract y from both sides to get 6 + 2y = 24.

Then you can subtract 6 from both sides to get 2y = 18.

Finally, divide both sides by 2 to get y = 9.

Determine the equation that this graph represent

Answers

y= 3/2x + 3



and slope = rise/run
Y=3/2+3

I hope that’s right.

Bryan has $15 to spend on taxi fare. The ride costs $5 plus $2.50 per mile. How many mile can Bryan go without spending all $15

Answers

Answer:

3 miles.

Step-by-step explanation:

He has to pay 5 just to ride, and 2.50 per mile.

2.50(x)+5=15

2.50(4)+5=15

10+5=15

So he can riide 3 miles without spending all his money.

What is the range of the function shown on the graph above

Answers

You did not attach a picture of the graph

Select all the expressions equivalent to:
20a + 10b
a
5(4a + 2b)
b
10(2a + b)
C С
2(10a + 5)
2(10a + 5b)
Od
Оe
5(4a - 2b)

Answers

Answer:

5(4a + 2b)

10(2a + b)

2(10a + 5b)

Step-by-step explanation:

we are trying to find equations equivalent to (20a + 10b), so distribute

5(4a + 2b) = 20a +10b YES

10(2a + b) = 20a +10b YES

2(10a +5) = 20a + 10 NO

2(10a + 5b) = 20a +10b YES

5(4a - 2b) = 20a - 10b NO

Adele rides her bike 28 miles in 3.5 hours. How far has Adele traveled on her bike if she rides for 8 hours?

Answers

Answer:

64 miles

Step-by-step explanation:

if you divide 28 by 3.5, this gives you the number of miles per hour, I got 8. Multiply that by 8 because that is the number of hours we are looking for and you get 64. That is the answer.

The team won 18 of its 30 games. What was the team’s won-lost ratio?

Answers

Answer:

18:12 (accurate)

3:2 (simplified)

Step-by-step explanation:

The team won 18 games out of 30 total games. Find the amount of games lost by simply subtracting 18 with 30:

30 - 18 = 12

The ratio you are trying to find is won to lost, or won:lost. Plug in the corresponding numbers to the corresponding terms:

won:lost ⇒ 18:12

18:12 is the ratio.

If the teacher asks you to simplify, factor both sides. Divide 6 from both sides:

(18)/6 : (12)/6

3:2

3:2 is your simplified ratio.

~

Bert is driving along a country road at a constant speed of 30 miles per hour. How long does it take for him to travel 50 miles?

Answers

30 miles/60 minutes = 50 miles/ x minutes
Cross multiply, and you have 3000 = 30x. x = 100 minutes, or 1 hour 40 minutes

The time of 1 hour 40 minutes Bert takes for him to travel 50 miles.

What is the distance?

Distance is defined as the product of speed and time.

What are Arithmetic operations?

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operation is called the arithmetic operator.

Operators which let do a basic mathematical calculation

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

Given that Bert is driving along a country road at a constant speed of 30 miles per hour

To determine the time it takes for him to travel 50 miles.

Let the time of x minutes it takes for him to travel 50 miles.

⇒ 30 miles/60 minutes = 50 miles/ x minutes

Cross multiplication apply in above equation,

⇒ 30x. x = 60x50

⇒ 3000 = 30x.

⇒ x = 100 minutes, or

1 hour 40 minutes

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Find the simplest form
2 2
+
9.7

Answers

there's a random space in between the 2 and 2. not sure if it's meant to be 2.2 or 22 but i'll do both.

2.2 + 9.7 = 11.9

22 + 9.7 = 31.7

Please help it is due today

Answers

i think answer is 8in2

please talk me my answer is correct or not

Answer:

8 inches squared

Step-by-step explanation:

4 3/4 of a cube + 4 1/4 of a cube + 4 whole cubes

4 + 4 = 8

-20 2 -6 -18 4 -4 put them from least to greatest

Answers

-20 -18 -6 -4 2 4 this is the answer
[-20, -18 , -6 , -4 , 2 , 4 ]

All rational numbers are whole numbers? True or false

Answers

Yes this is very true

CAN SOMEONE HELP ME PLEASE!!!

Answers

Answer:

i think this is right

Step-by-step explanation:

4

Target sells 3 apples $1.50 what is the cost of 20 apples

Answers

Answer:

$10

Step-by-step explanation:

1.50 divided by 3 = 0.50

0.50 x 20 = 10

Shandra had $200 in her bank account on Monday. On Tuesday, she had a
debit of $50 and a credit of $25. How much money does Shandra have in
her bank account on Wednesday?

Answers

Answer:

175

Step-by-step explanation:

0.009 in scientific notation

Answers

Answer:

9 x 10^-3

Step-by-step explanation:

Type the expression that results from the following series of steps:
Start with
x
, add 3, then times by 6.

Answers

Answer:

6x+18

Step-by-step explanation:

(x+3) * 6= 6(x+3)=6x+18

Answer:

6(x+3) or 6x +18

Step-by-step explanation:

x

add 3

x+3

times by 6

6(x+3)

simplify

6x+18


What is the y-intercept?

Answers

Y intercept is 8
I hope this helps

How can I know 20 digits of Π… ??

And not know the 10 digits of your phone number?

Answers

Answer - lol smooth 6273893

- 6w = 354 w=__?
-45= -9m m__?
h/9 = 36 h=__?
18 = y/7
y=__?
f/-4 = - 13 f=__?
15 = n/-3 n=__?

Answers

Answer:

I don't really understand the  question, there calculator websites you can use

Step-by-step explanation:

Carris is making necklaces to sell at a local craft fair. She makes the necklaces by hand, so she uses a table to determine how many beads to make for the necklaces.

Answers

The beads will make the necklace feel structured so i think 4 beads

Answer: 48

Step-by-step explanation:

Each is 8x? So 8x1, 8x2 so on, then you get 48!

5
Evaluate the expression when x = 3 and y = 6
The product of 8 and a number x

Answers

Answer:

46

Step-by-step explanation:

First, we must write the mathematical form for "the product of 8 and a number x":

8

×

x

Then "6 more than this" would be:

(

8

×

x

)

+

6

So, to evaluate for  

x

=

5

we substitute  

5

for  

x

and calculate:

(

8

×

5

)

+

6

40

+

6

46

Which expression is equivalent to x^2 - 64?

Answers

Answer:

X= 8 and X=-8

Step-by-step explanation:

x^2-64

spilt into (x-8)(x+8)

set both equal to 0

0=x-8

x=8

0=x+8

x=-8

A jogger is running with an initial speed of 5 m/s. The jogger then sprints to the finish line, increasing their speed to 10 m/s over 5 seconds. What is the jogger's acceleration in m/s squared?

Answers

Answer:

Step-by-step explanation:

1 m/s square

The numbers 1 to 5 are placed in a hat. What is the probability that you will pick the number 1 pm
4, and without replacing the number in the hat, select the number 3? Write your answer as a
simplified fraction. *

Answers

What grade are you in? Lord

Erik used 28 centimeters of tape to wrap 7 presents. How much tape will Erik need in all if he has to wrap 12 presents? Solve using unit rates.

Answers

Answer:

Length of tape required to wrap 12 presents is 48 centimeters.

Step-by-step explanation:

Length of tape required to wrap 7 presents = 28 centimeters

Length of tape required to wrap 1 present = [tex]\frac{28}{7}=4[/tex] centimeters

Therefore,

Length of tape required to wrap 12 presents = 12 × Length of tape required to wrap 1 present

= 12 × 4

= 48 centimeters

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