Find the particular solution to ty''-(1+t)y'+y=t^2e^t.

Answers

Answer 1

Complete Question

Find a particular solution to [tex]ty''-(1+t)y'+y=t^2e^t , t > 0[/tex]  

[tex]y_1 = 1 + t , \ y_2 = e^t[/tex]

   

Answer:

The solution is    [tex]y_p = -e^{2t} + t + \frac{3t^2}{2} + \frac{t^3}{2}[/tex]

Step-by-step explanation:

  Now the given equation is [tex]ty''-(1+t)y'+y=t^2e^t , t > 0[/tex]

             dividing through by  t

       We have  

         [tex]y'' - \frac{1 + t }{t}y' + \frac{1}{t} y = te^t \\\\ let's\ call\ it \ g(t)[/tex]

Now for the given initial value we can generate our Wronskian as follows

        [tex]W(y_1 ,y_2) = | \left y_1} \atop {y_1'}} \right. \left y_2} \atop {y_2'}} \right | = | \left {(1 + t)} \atop {1}} \right. \left e^t} \atop {e^t}} \right | = (1 + t )e^t - e^t = te^t[/tex]

Now applying  method of variation of parameters to obtain the particular solution

So here we assume that

          [tex]y_p = v_1 y_1 + v_2 y_2[/tex]

So

       [tex]v_1 = - \int\limits {\frac{y_2 (t) g(t)}{W(t)} } \, dt = - \int\limits {\frac{e^t te^t}{te^t} } = - \int\limits { e^t} } = -e^t[/tex]

And

    [tex]v_2 = - \int\limits {\frac{y_1 (t) g(t)}{W(t)} } \, dt = - \int\limits {\frac{(1 + t) te^t}{te^t} } = - \int\limits (1 + t) = t + \frac{t^2}{2}[/tex]

   

So

     [tex]y_p = -e^t * e^t + t + \frac{t^2}{2} * 1 + t[/tex]

     [tex]y_p  =  -e^{2t}   +  t +   \frac{3t^2}{2} + \frac{t^3}{2}[/tex]

   

     


Related Questions

What is the equation shown in standard form of the line shown on the graph?
O x = 4
O y = 4
O x - y = 4​

Answers

Answer:

[tex]y = 4[/tex]

Step-by-step explanation:

Because no matter what value x is, y is always 4

Please Help A) Find the perimeter B) The area of the rectangle

Answers

Answer:

A) 36.2m  B) 70m

Step-by-step explanation:

5.6m + 5.6m = 11.2 m

12.5 + 12.5= 25  11.2 + 25 = 36.2m

Length x width equals area

12.5m = length and 5.6m= width

multiply 12.5 x 5.6= 70m


Is the following number an integer?
30/6

Answers

Answer:

NO ! For 30, the answer is: No, 30 is not a prime number. The list of all positive divisors (i.e., the list of all integers that divide 30) is as follows: 1, 2, 3, 5, 6, 10, 15, 30.

Step-by-step explanation:

Given the points A(-5, -6) and B(8, 2), if C is the midpoint of segment AB, find the coordinates of the midpoint of segment CB

Answers

It’s c bucko I did that

The manufacturer of pencils spends $0.05 to make each pencil and sells them for 0.25. The manufacturer also has fixed
costs each month of $2000. Find the number of pencils x that the manufacturer needs to sell in order to break even

Answers

Answer:

x=10000

Step-by-step explanation:

The break even point occurs when costs equal revenue. Write the break-even formula and solve to find

C(x)0.05x−20000.2xx=R(x)=0.25x=2000=10000.

what value of x makes this equation true X over 3 = 24

Answers

Answer:

x=72

Step-by-step explanation:

Start with [tex]\frac{x}{3}[/tex]=24

Using the multiplication property of equality, multiply each side by 3

x=72

The answer is 72 it would be 72

A rectangle is 3 times as long as it is wide. The perimeter is 24 feet. Find the dimensions.

Answers

Answer:

Width is 3 units, The Length is 9 units.

Step-by-step explanation:

Three times as much as 3, or 9, is how you find the lengths. This being- 3+3=6 and 9+9=18, 6+18=24, which is the perimeter, therefore 3 and 9 are the dimensions.

fill in the table using the function rule: y=1 + 4x​

Answers

Answer:

13, 25, 37, 41

Step-by-step explanation:

By plugging each x value given for x, you are able to solve for y. Just multiply x by 4 and add 1.

13-25-36-41 is the answer

Which statements are true regarding f(x)=10/x+5

? Check all that apply.

The domain of f(x) is (–∞, –5) U (–5, ∞).
The range of f(x) is (–∞, 2) U (2, ∞).
The x-intercept is at (–5, 0).
The y-intercept is (0, 2). 
There is a vertical asymptote at x = –5.
The end behavior is  x → –∞, f(x) → 0 and x → ∞, f(x) → 0.

Answers

For the function   [tex]\frac{10}{x + 5}[/tex]  , we can say

The domain of f(x) is (–∞, –5) U (–5, ∞).

The y-intercept is (0, 2).

There is a vertical asymptote at x = –5.

The end behavior is  x → –∞, f(x) → 0 and x → ∞, f(x) → 0.  

What is a function?

A mathematical relationship from a set of inputs to a set of outputs is called a function.

What is domain of a function?

The domain of a function is the set of all possible inputs for the function.

What is range of a function?

The range of a function is the set of outputs the function achieves when it is applied to its whole set of outputs

What is asymptote?

An asymptote is a straight line that can be horizontal, vertical or oblique that goes closer and closer to a curve which is the graphic of a given function.

What is intercept?An intercept of any function is a point where the graph of the function crosses, or intercepts, the x-axis or y-axis.To find the x-intercept we need to do y = 0To find the y-intercept, we need to do x = 0

How to know the domain of function?

The given function is  [tex]\frac{10}{x + 5}[/tex]  

Now, if x = -5 then the function becomes undefined.

∴ The domain of the function is all real numbers except -5

So, The domain of f(x) is (–∞, –5) U (–5, ∞).

So, option a is correct.

How to know the range of the function?

Clearly, the range of the function includes all real numbers

So, option B is wrong

How to find the x-intercept?

To find the x-intercept , we will have to solve f(x) = 0,  which is not at all possible for this function.

So, option C is wrong

How to find the y-intercept?To find the y-intercept, we need to do x = 0

So, putting x = 0 in the function we get f(x) = 2

So, the y- intercept is (0, 2).

So, option D is correct.

How to find vertical asymptote ?To find the vertical asymptote, we need to make the                    denominator = 0

∴ x+ 5 = 0

∴ x = -5

So, there is a vertical asymptote at x = –5.

Hence option E is correct.

How to find the end behavior?

We can see,

As x tends to -∞, x + 5 will also tend to -∞We know that a number divided by ∞ or -∞ becomes 0

So, as x tends to -∞, f(x) will tend to 0

So, Option F is correct.

Find more about "Domain and Range of Functions" here: https://brainly.com/question/1942755

#SPJ2

Answer:

ADEF

Step-by-step explanation:

ADEF

Craig has acollection of 220 marbles. He lets his friend have 1/4 of his collection and sells 1/5 of his collection to the novelty store. He takes 15 marbles home to give to his brother. how many marbles remain in Craig's collection? ​

Answers

Answer:

he would have 106

Step-by-step explanation:

hope it helps

which decimal is less than 0.8 and greater than 0.02

Answers

Answer:

0.02<x<0.80

0.4

Step-by-step explanation:

0.02 is equal to 2/100 and 0.8 is equal to 80/100

so you could really choose any number between 0.03 and 0.79

Answer:

Less than 0.8 and greater than 0.02

0.8 > a > 0,02

There are many decimals:

0.7

0.67

0.6

0.5

0.4

0.3

0.2

0.1

0.023

0.021

and many others

What is the property of (4y + 1) x 0 =0

Answers

Answer: Zero Property

Step-by-step explanation:

27. Give the perimeter of the rectangle below in
simplest form.

Answers

Answer:

The permeter will be 26 units

Step-by-step explanation:

First to find this you need to know what the value of x is to do this I will use the equation 3x - 7 = x + 2

1. add seven to both sides leaving 3x = x + 9

2. Then subtract the 1x from both sides leaving 2x = 9

3. Then divide 9 by 2 which will be 4.5, x = 4.5

Then just plug 4.5 into each x value 4.5 + 2 and 3(4.5) - 7

1. 4.5 + 2 = 6.5

2. 3(4.5) - 7              13.5 - 7 = 6.5

The perimeter of the rectangle below in simplest form will be 4(x - 3).

Length of the rectangle = 3x - 7

Width of the rectangle = x+2

The perimeter of a rectangle is given as 2(length + width). The perimeter of the rectangle given will then be:

= 2(length + width)

= 2(3x - 7) + 2(x + 2)

= 6x - 14 + 2x + 4

= 4x - 12 = 4(x - 3)

Therefore, the perimeter of the rectangle in simplest form will be 4(x - 3).

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The rate of auto thefts doubles every 5 months.
(a) Determine, to two decimal places, the base b for an exponential model y = Abt of the rate of auto thefts as a function of time in
months.
(b) Find the tripling time to the nearest tenth of a month.
months

Answers

I think first one is the answer

mark me as branlist and follow me

what is the answer to
5 1/6 times ( -2/5)

Answers

Answer:-31/15

Step-by-step explanation: step 1: make both fractions improper

step 2: multiply numerator and denominator 31/6 x -2/5= -62/30

step 3: simplify -31/15

A box of books weighs 4.10 kg for every meter of it's height. Convert this ratio into pounds per foot.

Answers

Answer:

The ratio is   k  =   2.76 pounds /  foot

Step-by-step explanation:

From the question we are told that

   For  1 m  height  =>  4.10 kg mass

generally  1 meter = 3.28084 feet  

Also

  1 kg  = 2.20462 pound

  4.10 kg  =  x pounds

So

      [tex]x = \frac{4.10 * 2.20462}{1 }[/tex]

=>    [tex]x = 9.04 \ pounds[/tex]

So

        9.04 pounds  = 3.28084  feet  

         z pounds  =  1 foot

So  

       [tex]z = \frac{ 9.04 * 1 }{ 3.28084}[/tex]

=>   z = 2.76 pounds

So the ratio is in pounds per foot is

      k  =   2.76 pounds /  foot

       

The value of -31.45/-3.21 is around?

Answers

My calculator says 9.797507788, so you can just round to 9.8

James has 1,836 marbles. He decides to divide them equally among 23 boxes. How many marbles will James have left over?

Answers

Answer:

79.8260869565

Step-by-step explanation:

When dividing 1,836 by 23= 79.8260869565

Which of the following inequalities is incorrect?
00>-2
6 >-12
-5<-8
0-7<-5

Answers

Step-by-step explanation:

First, is 0 greater than -2? Correct

Next, is 6 greater than -12? Correct

Is -7 less than -5? Correct

Finally, is -5 less than -8? NERP!!

So C. is incorrect. Or in this case, it is...

A candy store sells mints in 14, 12 , and 34 lb packages. John purchases several packages of each weight.

What is the weight of 6 packages of the 14 lb package?

Answers

Answer:

84 lbs

Step-by-step explanation:

Multiply 14*6 to get the total weight

Find the sum of the squared residuals for each potential line of fit, and then determine which potential line is the true line of best fit. Equation 1 Square of residual .28 .167 .19 Equation 2 Square of residual .005 .110 .09 Equation 3 Square of residual .125 .125 .26 Equation 4 Square of residual .212 .009 .08 Question 8 options: Equation 4 Equation 1 Equation 3 Equation 2

Answers

Answer: Equation 2

Step-by-step explanation:

Equation 1 Square of residual .28 .167 .19

Sum of Square Residual :

( .28 + .167 + .19) = 0.637

Equation 2 Square of residual .005 .110 .09

Sum of Square Residual :

(.005 + .110 + .09) = 0.205

Equation 3 Square of residual .125 .125 .26

Sum of Square Residual :

( .125 + .125 + .26) = 0.51

Equation 4 Square of residual .212 .009 .08

Sum of Square Residual :

( .212 + .009 + .08) = 0.301

Equation 2 is the best potential line of best fit as it has lowest value of sum of square residual. And the best line of fit is one which the sum of Squared error is lowest.

Which of the following trinomials could represent the product (x + m)(x + n) if m = 5 and n = -7? A x2 + 2x - 35 B x2 - 12x - 35 Cx2 + 35x + 2 D x2 - 2x - 35

Answers

Hey there! I'm happy to help!

Let's plug in these values.

(x+5)(x-7)

We use the FOIL method to multiply the two.

We multiply the Firsts.

x·x=x²

We multiply the Outsides.

-7·x=-7x

We multiply the Insides.

5·x=5x

And we multiply the Lasts.

-7·5=-35

We combine these all.

x²-7x+5x-35

x²-2x-35

Have a wonderful day! :D


You are buying tickets to a Star Wars Convention. The tickets cost $10 per adult and $3 per child. Parking is a one-time fee of $5. If you
purchased two adult tickets, a, and the total cost was $109, how many child tickets, c, were purchased?

Answers

Answer:

28 children tickets

Step-by-step explanation:

$109 for the whole cost

bought 2 adult tickets that costed 10$ each and payed 5$ for parking fee

add them together 25$

109-25 =84

84/3 =28

Assuming that a local cost cutter provides cuts perms and hair styling service and you fix cost are $120,000 in the variable cost or 40% of the sales revenue last year’s revenue total of $250,000. What is the break even points in sales dollars?

Answers

Answer:

Unit selling price

$7 $9 $7

Unit variable costs

(4) (5) (1)

Unit contribution margin

$3, $4, $6

With monthly fixed costs of $306,000, the company sells two units of A for each unit of B and three units of B for each unit of C.

Evaluate =f(×) r 6x-2 for f (2a-3)​

Answers

The first option 12a - 20

Answer:

[tex] \boxed{\sf f(2a - 3) = 12a - 20} [/tex]

Step-by-step explanation:

Function given:

⇒f(x) = 6x - 2

Substitute 2a - 3 into the function in place of x:

⇒f(2a - 3) = 6(2a - 3) - 2

Expand bracket:

⇒f(2a - 3) = 12a - 18 - 2

Add the like terms:

⇒f(2a - 3) = 12a - 20

Graph the linear equation by finding its intercepts.
3x + 6y = 18

Answers

x intercepts are (6,0)
y intercepts are (0,3)

OMG! I just answered the wrong question... so sorry

There are 6 black marbles, 14 blue marbles, 8 white marbles,
and 12 clear marbles in a bag. If Andy chooses a second marble
without replacing the first marble, what is P(black, then clear)?

Answers

Answer:

3/65 = 0.046 = 4.6%

Step-by-step explanation:

Notice that the total number of marbles is:

6 + 14 + 8 + 12 = 40

Then , the probability of getting a black marble first is 6/40 = 3/20

Now, since the experiment is without replacing, he is left with a total of 39 marbles in the bag, and the probability of getting a clear one is now 12/39

The total probability is the product of these two:

(3/20) x (12/39) = 3/65 = 0.046 = 4.6%

Order from greatest to least 1.202;1.29;1.02

Answers

Answer:

1.29, 1.202, 1.02

Step-by-step explanation:

1.29
1.202
1.02
hope this helps

Help solve step by step please? 3/7➗4/5=

Answers

Answer:

15/28

Step-by-step explanation:

Step-by-step explanation:

3/7 divided by 4/5

Find the reciprocal of 4/5 which is 5/4

Multiply 3/7 by 5/4

3*5= 15 which is the numerator

7*4=28 which is the denominator

so the final answer is 15/28

The perimeter of a rectangle is 40 m. The length is 4 m more than three times the width. Find the length and the width of the rectangle.

Answers

Answer:

Width = 4 m, Length = 16 m

Step-by-step explanation:

Perimeter = 40

Width = x

Length = 3x + 4

x + x + 3x + 3x + 4 + 4 = 8x + 8

40 - 8 = 32

32/8 = x

x = 4

Width = 4

Length = 16

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