Solve the differential equation: y"-5y'+6y=0

Answers

Answer 1

The solution to the differential equation in this problem is given as follows:

y(t) = Ae^(3t) + Be^(2t).

How to solve the differential equation?

The differential equation for this problem is given as follows:

y'' - 5y' + 6 = 0.

It is a simple linear and homogeneous second order differential equation, hence it can be solved with the characteristic equation method.

The characteristic equation for the differential equation is given as follows:

r² - 5r + 6 = 0.


The roots for the characteristic equation are obtained by finding the linear factors and using the factor theorem as follows:

(r - 3)(r - 2) = 0.

Hence:

r - 3 = 0 -> r = 3.r - 2 = 0 -> r = 2.

These are real and non-repeated roots, hence the solution is given as follows:

y(t) = Ae^(3t) + Be^(2t).

In which A and B are constants depending on the initial conditions for the differential equation.

More can be learned about differential equations at https://brainly.com/question/18760518

#SPJ1


Related Questions

4.) Fill in the table to show a proportional relationship and then identify the
constant of proportionality for the cost to the number of yoga classes. In
the answer box, please list the constant of proportionality.

Answers

Answer/Step-by-step explanation:

✔️Number of Yoga classes = x

Cost ($) = y

Constant of proportionality (k) = y/x

Using the pair form the table of values given, (4, 60), find the constant of proportionality:

✅k = 60/4 = 15

Equation that represents the relationship between x and y is:

y = 15x

✔️Let's complete the table.

✅When number of yoga classes (x) = 2:

Substitute x = 2 into y = 15x

Thus,

y = 15*2 = 30

That is, 2 Yoga classes will cost $30

✅When number of yoga classes (x) = 6:

Substitute x = 6 into y = 15x

Thus,

y = 15*6 = 90

That is, 6 Yoga classes will cost $90

✅When number of yoga classes (x) = 8:

Substitute x = 8 into y = 15x

Thus,

y = 15*8 = 30

That is, 8 Yoga classes will cost $120

SOMEONE PLEASE ANSWER 3 ITS DUE IN 3 MINUTES!! WHOEVER ANSWERS GETS BRAINLIEST

Answers

Answer:

9:10

Step-by-step explanation:

74 is the buccaneers, and 35+45=80

so the ratio is 74:80

simplify to 36:40

then to 18:20

then to 9:10

The price of a toy costing £50 is increased to £65
work out the percentage increase

Answers

Answer:

Percent increase = 30%

Step-by-step explanation:

Given that:

Old price of toy = £50

New price of toy = £65

Difference = New price - Old price

Difference = 65 - 50

Difference = £15

Percent increase = [tex]\frac{Difference}{Old\ price}*100[/tex]

Percent increase = [tex]\frac{15}{50}*100[/tex]

Percent increase = 0.3 * 100

Percent increase = 30%

Hence,

Percent increase = 30%

Workout the size of angle x 79 35

Answers

Answer:

66 degrees

Step-by-step explanation:

Add both of those angels. 79+35=114

And then every triangle equals 180 so subtract

180-114=66

2. A triangle has sides of lengths 15, 23, and 28. Is it a right triangle? Explain.
A. No; 152 + 232 = 282
C. Yes; 152 +232 +282
B. No; 152 +232 +282
D. Yes; 152 + 232 = 282

Answers

Answer:

A

Step-by-step explanation:

the sum of the square of the legs of a right triangle equal the square of the third side:  a² + b² = c²

15² + 23² ≠ 28²

...................................................................................................................................................................

Answers

....................(67(,8,85,8(,84.8;.8;,7;,7;,6: ye urcurcfuz
Du

Answer:

stan stray kids periodt

The ratio of cars to trucks in a parking lot is 2:5. If there are 254 cars, how many trucks are in the lot? What is the answer plz

Answers

Answer:

635 trucks

Step-by-step explanation:

So first e know the ratio is 2:5

The amount of cars are 254

So the 2 in the ratio which represents cars is 254

So w can make that as A ratio

2:254

The 5 is known but the actual amount is unknown so we can make that x

5:x

Now we gotta make them equal to each other

2:254=5:x

Turn into fraction

2/254=5/x

Cross multiply (proportion)

2x=1270

Solve

x=635

So 635 trucks

Evaluate the algebraic expression 1.5t -7.2 for each given value 6 -5

Answers

Answer:

1.8 ; - 14.7

Step-by-step explanation:

Evaluate the algebraic expression 1.5t -7.2 for each given value 6 ; -5

For each of values 6 and - 5 ;

Substitute the values for t in the expression ; 1.5t - 7.2

Substituting 6 for t:

1.5(6) - 7.2

9 - 7.2

= 1.8

Substituting -5 for t:

1.5(-5) - 7.2

-7.5 - 7.2

= - 14.7

5) The probability that a typist makes 0, 1, 2, 3, 4, or 5 mistakes on a page are, respectively

0.09, 0.11, 0.24, 0.21, 0.17, 0.05. What is the probability that the typist makes three or more

mistakes mistakes on a page.

Answers

Answer:

0.43

Step-by-step explanation:

Formatting the Given data into a probability distribution table :

X : ____ 0 __ 1 ___ 2 ____ 3 _____ 4 ____ 5

P(x) : _0.09_0.11 _ 0.24 _0.21 ___ 0.17 __ 0.05

Probability of making 3 or more mistakes :

P(x ≥ 3) = P(x = 3) + P(x = 4) + P(x = 5)

P(x ≥ 3) = 0.21 + 0.17 + 0.05

P(x ≥ 3) = 0.43

How many different triangles can you make if you are given three lengths for sides?

Answers

Answer:

The lesson Triangle Construction discussed how to make a triangle given three side lengths. As you discovered, as long as two of the lengths added up to be greater than the third, they would form a unique triangle (only one triangle could be formed).

Step-by-step explanation:

Can you give a picture of what you're talking about so I can help? lol.

Please help me answer this question. There’s a picture attached.

Answers

this is isosceles triangle, so side AB and BC are the same !

9x-8 = 28

9x=36

x=4

Answer:

probably 4 since the sides are the same

Step-by-step explanation:

9x-8=28

28+8=36

9x=36

36÷9=4

x=4

Here is a list of ages (years) of children in a room: 2, 6, 5, 9, 6, 7, 2 State the median.

Answers

The median is 9 bc it’s in the middle

Amanda bill and Hong since a total of 80 text messages during the weekend bill sent eight more messages than Amanda Hong sent two times as many messages as Amanda how many messages did they each send

Answers

Answer:

amanda: 18

Hong: 36

Bill: 26

Step-by-step explanation:

a+b+h=80

b=8+a

H=2A

a+8+a+2a=80

4a+8=80

a=18

What is the y-intercept?

Answers

Answer:

the y intercept is where the line crosses the y axis

what the person said above was correct, you can look it up

Please help I'm so confused​

Answers

Answer:

the quotient is 805. the remainder is 5.

Step-by-step explanation:

when you multiply the 8 you put the number you multiplied on top. The first one is 80 and then 5. You have a 5 left over which makes that the remainder

Answer:

1. is 85.625

2. is .625

so you divide 685 and you know nothing multiplied by 8 will equal 685 so the remainder is 685

how are meiosis and mitosis different

Answers

Answer:

meiosis is the result of four cells dividing

mitosis is the result of 2 identical cells

Step-by-step explanation:

not 100% sure but i hope this helps <3

5x + y = 9
3x + 2y = 4
Solve with elimination method

Answers

Answer:

x=2 y=-1

Step-by-step explanation:

multiply the top equation by negative 2. then it is -7=-14

then you dive and find out that x=2 and plug it inot the equation and solve for x 10+?=9 which is -1

Answer:

x=2

y=-1

Step-by-step explanation:

make it so that you can cancel out the y

to do this multiply the top equation by 2

10x+2y=18

3x+2y=4

subtract to get rid of 2y

7x=14

x=2

substitute the x into one equation

3(2)+2y=4

6+2y=4

2y=-2

y=-1

\left(6x10^2\right)\div \left(3x10^{-5}\right)

Answers

Answer:

[tex]\frac{6\times 10^2}{3\times 10^{-5}}[/tex] = 2 x 10⁷

Step-by-step explanation:

Given expression is [tex]\frac{6\times 10^2}{3\times 10^{-5}}[/tex]

The given expression is simplified as follows;

[tex]\frac{6\times 10^2}{3\times 10^{-5}} = (\frac{6}{3} )\times 10^{2-(-5)}\\\\(\frac{6}{3} )\times 10^{2-(-5)} = (\frac{6}{3} )\times 10^{2+5}\\\\(\frac{6}{3} )\times 10^{2+5} = 2 \ \times \ 10^7[/tex]

Therefore, the result of the given expression is 2 x 10⁷

Write two equations, one with an x-intercept
but no y-intercept, and one with a y-intercept but no x-intercept. ( how do I do number 9 can sum1 give me the answer or help me pls)

Answers

Answer:

No X-intercept: √(x)+1

No Y-intercept:   √(x-1)

Step-by-step explanation:

To solve this you need to have some knowledge about a  bunch of parent graphs and so this question is kind of hard to explain

Can someone please help

Answers

Answer : y = -3/4x + 1

To find an equation that goes through the two points provided, you have to find the slope using those same two points.
The equation for slope is (y2-y1)-(x2-x1).

The slope is -3/4.

The y-intercept is already given to you in the point (0,1).

Just plug everything into an equation and you get y = -3/4x + 1.

You deliver flowers to an office building. You enter at ground level and go down 4 floors to make the first delivery! Then you go up 6 floors to make the second delivery. Write down integer that represent how you return to ground level.

Answers

Answer:

-2

Step-by-step explanation:

you went to floor -4 in the begining, then went up 6 floors to floor 2

-4+6=2

so now you have to go down 2 floors making it negative

no your answer is -2

A certain car can travel 28.45 miles with one gallon of gasoline. The gasoline tank can hold

11.5 gallons. How many miles can this car travel on a full tank of gas? SHOW YOUR WORK!

Answer:

Answers

Answer:

327.175 miles

Step-by-step explanation:

Step one:

given data

A car can travel 28.45 miles with one gallon of gasoline

We want to find how far the car can go with 11.5 gallons

Step two:

        if 1 gallon can go 28.45 miles

then 11.5gallons will go x miles

cross multiply we have

1x= 28.45*11.5

x=327.175 miles

Write the exponent for the expression.
1/8 x 1/8

Answers

Answer:

[tex]8^{-2}[/tex]

Step-by-step explanation:

[tex]2^{-2} = 1/4[/tex]

So:

[tex]8^{-2} = 1/8*1/8[/tex]

How much does the nylon rope cost per meter?

Answers

Answer:

(a) $0.80

(b) 1.25 m

Step-by-step explanation:

(a) Put 1 where L is, and evaluate the equation.

... p = 0.8·1 = 0.8

The cost for 1 meter of rope is $0.80.

(b) Put 1 where p is and solve for L.

... 1 = 0.8L

... 1/0.8 = L = 1.25

The length of rope that costs $1 is 1.25 meters.

Answer:

Well that depends on where you buy it

Step-by-step explanation:

It could cost various things and you didn't add enough context for us to assume where you could have purchased the nylon rope

If the supplement of <1 is 32º less than the measure of <1, what is m<1? a 1060 b 74o c 61o d 29o

Answers

Answer:

a. 106 degrees

Step-by-step explanation:

m=measure of angle 1; m-32 degrees=measure of supplement

m+(m-32 degrees)=180 degrees Add 32 degrees to each side.

2m=212 degrees Divide each side by 2

m=106 degrees ANSWER: The measure of angle 1 is 106 degrees

 

CHECK:

106+(106-32)=180

106+74=180

180=180

In one day a store sold 3/4 as many DVDs as Blu-Ray discs. The total number of DVDs and Blu-Ray discs sold that was 406. How many DVDs were sold

Answers

Answer:

283.2

Step-by-step explanation:

The number of DVDs will be 304.5.

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that In one day a store sold 3/4 as many DVDs as Blu-Ray discs. The total number of DVDs and Blu-Ray discs sold was 406.

The number of the DVDs will be calculated as below:-

Number = 406 x ( 3 / 4).

Number = 304.5

Therefore, the number of DVDs will be 304.5.

To know more about an expression follow

https://brainly.com/question/17220365

#SPJ2

how do you figure out what type of solution it is when their are 2 ordered pairs

Answers

Answer:

To figure out if an ordered pair is a solution to an equation, you could perform a test. Identify the x-value in the ordered pair and plug it into the equation. When you simplify, if the y-value you get is the same as the y-value in the ordered pair, then that ordered pair is indeed a solution to the equation.

Step-by-step explanation:

What type of number is this: 5 3/4?

Answers

Answer:

it’s mixed number

Step-by-step explanation:

Answer:

It is a Mixed number!

Step-by-step explanation:

Find three consecutive integers such that the sum of the first and twice the second is 68 minus three times the third.

Answers

Answer:

x=9.5

Step-by-step explanation:

x+2(x+1)=68-3(x+3)

x+2x+2=68-3x-9

3x+2=68=59-3x

6x=57

x=9.5

A 75 inch pipe is cut into two peices. One peice is two times the length of the other find the length of the shorter pipe

Answers

I could be very wrong but I believe it’s 25

You can divide 75 by 3 and that will give you 25 and if the pieces were even they would be 37.5 but the shorter one is 2 times shorter
Other Questions
I think I got this wrong I need help what is this plz help these teachers are impossible y>x+3y>4-x A rectangular prism has a volume of 30 cubic inches.It's length is 1/3and it's width is 3 feet. What is the height? Our nation watched our new President of the United States get sworn into office on Wednesday, January 20, 2021. What do you want to see come from our new leadership in our country? What are your hopes or maybe fears that you have in regards to our new leaders? (PLEASE DONT ARGUE!! This is all your opinion!) Can someone please help me with this. The first person who answers this gets brainliest . What is the difference between a linear function and a linearequation? The following code will not compile. Which of the options below would allow the code tocompile and run as intended?if (x >= -10 and < 10):print("In range") Jonathan buys 400 grams of trail mix that contain 18% cashew nuts. He mixes it with 200 grams of trail mix that contain 7% cashew nuts. How many grams of cashews are in the second mix? How were the Romans like the Greeks? What is sin R ?I have no idea how to solve According to "Introduction to Cultural Rebellion: Mid-Twentieth-Century Voices," what is a key element in the writing of postwar confessional poets and beat generation authors?support for anticommunist hysteriasupport for the development of consumerismsupport for individual human experiencessupport for the cultural ideal of the era Each of two dulicated strands of a chromosomes is called a Sphere of influence definition in history 27819= give me the quotient for 27819 Which of these is the BEST definition of sovereignty? A) limited power that has no geographical bounds B) A geographical area where no one is in power C) A group of people who have little power D) Ultimate power over a geographic area In your own words, what is the difference between an equation and an expression? What do these two changes have in common? your breath becoming visible on a cold day building a tower out of magnetic blocks What is the value of x? Unlike eukaryotes, prokaryotes do not have: A. DNA B. cytoplasm C. cell walls D. a membrane bound nucleus All of the following expressions are equivalent except _____. (5 - 5) x -5( x - 1) -5 x + 5 5 - 5 x