Find the solution of the second-order linear differential equation that satisfies the given initial conditions. y'' + 6y' + 9y = 0 y(0) = 0 y'(0) = 1

Answers

Answer 1

Answer:

The solution of this differential system is [tex]y(x) = x\cdot e^{3\cdot x}[/tex].

Step-by-step explanation:

This second-order differential equation is homogeneous and linear of the form:

[tex]y'' + p\cdot y' +q\cdot y = 0[/tex] (1)

Where:

[tex]p[/tex] - First-order constant coefficient, dimensionless.

[tex]q[/tex] - Zero-order constant coefficient, dimensionless.

Whose characteristic polynomial is:

[tex]\lambda^{2}+p\cdot \lambda + q = 0[/tex] (2)

Where [tex]\lambda[/tex] contains the roots associated with the solution of the differential equation.

If we know that [tex]p = 6[/tex] and [tex]q = 9[/tex], the roots of the characteristic equation are, respectively:

[tex]\lambda^{2}+6\cdot \lambda + 9 = 0[/tex]

[tex](\lambda +3)\cdot (\lambda + 3) = 0[/tex]

Which means that [tex]\lambda_{1} = \lambda_{2} = 3[/tex] and the solution of the differential equation is of the form:

[tex]y(x) = e^{3\cdot x}\cdot (c_{1}+c_{2}\cdot x)[/tex] (3)

Where [tex]c_{1}[/tex] and [tex]c_{2}[/tex] are integration constants.

The first derivative of the equation above is:

[tex]y'(x) = 3\cdot e^{3\cdot x}\cdot (c_{1}+c_{2}\cdot x)+c_{2}\cdot e^{3\cdot x}[/tex] (4)

Now, if we get that [tex]y(0) = 0[/tex] and [tex]y'(0) = 1[/tex], then the system of equations to the solved is:

[tex]c_{1} = 0[/tex] (3b)

[tex]c_{1}+c_{2} = 1[/tex] (4b)

The solution of this system is: [tex]c_{1} = 0[/tex], [tex]c_{2} = 1[/tex]. Therefore, the solution of this differential system is [tex]y(x) = x\cdot e^{3\cdot x}[/tex].


Related Questions

Pls help ASAP WILL GIVE BRAINEST :/

Answers

Answer:

6+7(b-1)=5+b
6+7b-7=5+b
-1+7b=5+b
7b-b=5+1
6b=6
6b/6=6/6
b=1

Step-by-step explanation:

b=1 the person above or below me has the explanation

can u pls help me with this question ​

Answers

Answer:

The correct answer is D, 6/8.

Step-by-step explanation:

For ratios or fractions an equivalent fraction has the same value but just more pieces. Think of it like a pizza. But to make sure they are equivalent you have to multiply or divide them by a fraction equal to 1. In other words the numerator and the denominator have to be the same number. So, when we multiply 3/4 by 2/2 you get 6/8 because 3 x 2 = 6 (numerators) and 4 x 2 = 8 (denominators).

If you have any additional questions please don't hesitate to ask me or your teacher to be sure you master the subject. Stay safe and please mark brainliest! :)

A triangle has angles of 30° 60° and 90° It is dilated by a scale factor of three give the angle measures of the dilation of the triangle

Answers

The scale factor will create a similar triangle and thus there will be no change in angles so angles will still be 30° 60° and 90°.

What is the scale factor?

You must specify the extent of the shape's enlargement when describing one.

The scale factor is the ratio of two dimensions such that one figure is large and another is small.

The scale factor is done due to the unpractical measurement of any figure.

Scale factor gives either a small or big similar image of a triangle, for example, if we have a triangle with vertices 2,4,6 and it is scaled by 1/2 then the resultant dimension will 1,2,3 but angles still remain the same.

Hence "The scale factor will create a similar triangle and thus there will be no change in angles so angles will still be 30° 60° and 90°".

To learn more about scale factors,

brainly.com/question/22312172

#SPJ1

which term of the series 2187,729,243...is 1/9​

Answers

Answer:

Step-by-step explanation:

Givens

a = 2187

r = 1/3

L = 1/9

what is n

Formula

L = a*r^(n-1)

1/9 = 2187 * (1/3)^(n-1)

1/(9 * 2187) = (1/3)^(n - 1)

1/19683 = (1/3)^(n - 1)

=================

You need to break 19683 down into its prime factors.

19683 = 3* 729

19683 = 3 * 3 * 243

19683 = 3 * 3 * 3 * 81

81 = 3^4 so there are 4 more threes in the breakdown.

19683 = 3 * 3 * 3 * 3 * 3 * 3 * 3

1/19683 = 1/(3)^(7-1)

1/9 is the 6th term in the series.

Make w the subject of the formula y - aw = 2w - 1

Answers

Answer:

[tex]w=\frac{y+1}{a-2} (a\neq 2)[/tex]

Step-by-step explanation:

[tex]y - aw=2w-1\\y-aw-2w=-1\\-aw-2w=-1-y\\-w(a-2)=-(y+1)\\w(a-2)=y+1\\w=\frac{y+1}{a-2} (a\neq 2)[/tex]

Hope this helps!

Two-thirds of the fruit in a basket are apples. One-fourth of the apples are green apples. What fraction of the fruit in the basket are green apples?

Answers

Answer:

1/6

Step-by-step explanation:

2/3*1/4

=2/12

=1/6

PLS GIVE BRAINLIEST

First, we need to find the least common denominator. This would be 12. So, our new fractions would be 8/12 and 3/12. We know that 8/12 of the basket are apples, and we need to take away the 3/12 of the green apples. This means there are 5/12 of the red apples.

Hope this helps :)

4n-(7-6n)


Helppp plz

Answers

4n - (7-6n)
4n -7 +6n (multiply minus to 7-6n)
10n -7 is the answer

I need help plz!!!!!! Will give 100 points.
Point-Slope Form: y - 5 = 3(x - 1)
Standard Form: ???? HELP

Answers

Answer : y = 3x + 2.
Explained : Distribute 3 to what’s inside of the parenthesis. Now you have y - 5 = 3x - 3. Add 5 to both sides and you have y = 3x + 2. Final answer.


What is an equation for the line that passes through the points (-2, 3) and (2, 1)

Answers

First find slope
(1-3)/(2+2) = -2/4 = -1/2
Y = -1/2x + b, plug in point
3 = -1/2(-2) + b
3 = 1 + b, b= 2
Final equation: y = -1/2x + 3

Help plzzzz will give brainliest

Answers

Answer:

It's positive.

Step-by-step explanation:

There are many reasons.... but one of the obvious ones is that it would've shown negative, correct?

It’s positive. Both the x and y axis continue to go up

increase 120 by 5% (answer)​

Answers

Answer:

what is question is this the question

Answer:

126

Step-by-step explanation:

[tex]\frac{5}{100}[/tex] × 120 = 6

120+6= 126

Help me with this please

Answers

Answer:

101.5m left to use after the big top goes up.

Step-by-step explanation:

18*10=180  [tex]\pi[/tex]r[tex]x^{2}[/tex]= 3.14*5^{2}=3.14*25=78.5

180-78.5= 101.5m

The proportion of observations from a standard Normal distribution that take values larger than -0.75 is about A) 0.2266 B) 0.7704 C) 0.7734 D) 0.7764 E) 0.8023

Answers

Answer:

Option C: 0.7734

Step-by-step explanation:

From z-distribution table attached,

P(Z ≤ -0.75) = 0.2266

However, we are looking for proportion of observations from a standard Normal distribution that take values larger than -0.75.

Thus;

P(Z > -0.75) = P(Z ≤ 0.75) = 1 - 0.2266

P(Z > -0.75) = 0.7734

Option C is the correct answer.

Help me out please I beg you

Answers

Answer:

tesrdxtcfygvoubucewh cwcs wuehcbwch w

Step-by-step explanation:

w edch dwjbsxchwej chwxc

can someone answer these?

Answers

Answer:

1. SSS

2.SSA

3.ASA

Step-by-step explanation:

For number one there is three congruent sides with the on in the middle

For number two there is two sides and one angle congruent

And number three has an embedded side between the two angles

Helllppppppp. A wheelbarrow has a wheel with a diameter of 10 in. What is the distance, in
inches, that the wheelbarrow moves after 16 full rotations of the wheel?

Answers

Answer:

160 in.

Step-by-step explanation:

10 *  16 = 160

hellpppppp please I will give brainliest​

Answers

Answer:

I think the answer is y=2x-2

Hope it is correct! The x is positive because the angle is pointing to the right, and the -2 came from the position of the line.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

WHATS A FUTURE FUNKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK

500,325+6,773,500,135

Answers

Answer: future the time or a period of time following the moment of speaking or writing; time regarded as still to come.

Step-by-step explanation:

Quick answer please!!!! Brodie hires a technician to fix his air conditioning unit. The total cost includes $26.50 for parts and $50.00 per hour the technician works on the job. Which equation can be used to find y, the total cost Brodie pays, given x represents the number of hours the technician works on the job? y=26.50x−50 y = 26.50x + 50 y = 50x + 26.50 y=26.50(x+50)

Answers

Answer:

y = 50x + 26.50

Step-by-step explanation:

we put the x after 50 be cause we don't know how many hours he worked

then add 26.50 the cost of the parts.

Hoped this helped.

Answer:

C: y=50x+26.50

Step-by-step explanation:

I just took the test and i got it right!!! 100%

do i get brainlest

If $2,500 is invested at 12% annual interest, which is compounded continuously, what is the account balance after 3 years, assuming no additional deposits or withdrawals are made?

Answers

Answer: 3,583.32

Step-by-step explanation:

Use money chimp calculator

Solve each equation. y + 20 = 7

Answers

Answer:

I Meant y =  -13

Step-by-step explanation:

Answer:

y= -13

Step-by-step explanation:

-13 plus 20 is 7

plug the -13 in where the y is and do the equation

-13+20=7

Missy wants to find the surface area of a snack box in her pantry her work is shown below

Answers

Answer:

Step 2: Missy did not multiply the area of each face by 2 before adding.

Step-by-step explanation:

I took the test :)

what function best models the data and what wil be the chicken breast after 50 miutes​

Answers

Answer:

Students use linear, quadratic, and exponential functions to model data from tables and choose the regression

most appropriate to a given context. They use the correlation coefficient to determine the accuracy of a

regression model and then interpret the function in context. They then make predictions based on their model

and use an appropriate level of precision for reporting results and solutions.  

Lesson 7 focuses on data sets that cannot be modeled accurately, and students are asked

to articulate why. Students use skills learned in Lesson 14 of Module 2 (where they used

calculators to write linear regressions) and apply similar techniques for data sets that are

better suited to modeling with quadratic or exponential regressions. Students use that

same technique to find linear regressions and use their graphing calculators to examine

the correlation coefficient and to find quadratic and exponential regressions. They

compare correlation coefficients to determine which model is best for the data.

Ultimately, students choose the regression model (linear, quadratic, or exponential) most

appropriate to a given data set and then write, verify, and interpret these models in

context. Students need a graphing calculator to complete this lesson. Graphing calculator

instructions are provided, but steps may vary slightly depending on the model of the

graphing calculator.

Refer to the following full modeling cycle during this lesson (Found on page 61 of the CCLS

and page 72 of the CCSSM).

Scaffolding:

 Students are more

engaged when working

with relevant and real data

that interests them.

Websites that provide

data sets are a good

resource for classroom

investigations.

 This lesson might need to

be divided into two days if

students need more time

to master the technology.

Step-by-step explanation:

In a group of 20 students, there are 7 boys. What is the ratio of girls to boys?

Answers

Answer: percent is 0.53%

The ratio is 7 to 13 so you just divide 7/13

Step-by-step explanation:

HELP ME ASAP!
What is the result when the number 44 is decreased by 75%?

Answers

Answer:

11

Step-by-step explanation:

Earl runs 60 meters in 40 seconds. How many meters per second does Earl run?

Answers

Earl runs 1.5 meters per second.................

During the winter months, heating bills can be expensive. A contractor claims that installing a new brand of insulation will considerably lower your heating bill (which was $205 last month). After conducting the test (assuming the data were provided). you find that the results are significant at the 5% level. You may also conclude: __________.a. the test would also be significant at the 10% level. b. the test would also be significant at the 1% level. c. both of the above. d. none of the above.

Answers

Answer:

The correct option is  a

Step-by-step explanation:

Generally the null hypothesis is  rejected (that the result is significant ) when the p-value is less that the the level of significance

Now from the question when the the level of significance was 5% the p-value was less than the level of significance so also when the level of significance is   10% the p-value will be less than the level of significance hence null hypothesis will also be rejected at this level(that is the result will also  be significant at the level of significance )  

Which best describes the error in solving the system of linear equations?
Only the x-value is given.
The wrong value for x is given.
The blue line is graphed incorrectly.
The red line is graphed incorrectly.

Answers

Answer:

a. Only the x-value is given.

Step-by-step explanation:

Taking a look at the graph of both equations, both equations are graphed correctly, because the slope (m) and y-intercept (b) values corresponds of each equation corresponds with what we have on the graph representing each equation.

The solution of two linear equations ought to be in a coordinate pair, (x, y). This means the x-value and it's correaponding y-value of the solution needs to be stated, not just the x-value.

Thus, the correct solution. Of the two linear equations are x = 4, when y = 3.

Solution in coordinate pair form is (4, 3).

Therefore, the statement that describes the error is:

a. Only the x-value is given.

which two triangles are congruent? complete the congruence statement.​

Answers

The two at the top not the one at the botton

This graph shows linear
y = f(x) and y = g(x).

Find the solution to the equation f(x) - g(x) = 0

Answers

Step-by-step explanation:

This graph shows linear

y = f(x) and y = g(x).

Find the solution to the equation f(x) - g(x) = 0

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