Mathematics High School

Given y1(t) = t^2 is a solution to: t^2y'' - 4ty' + 6y = 0, t > 0 find another solution using the method of reduction of order.

Answers

Answer 1

For a second order differential equation t²y'' - 4ty' + 6y = 0, general solution is of the form y(t) = c₁t² + c₂t³, so another solution other than y₁(t) = t² is y₂(t) = t³.

Given solution to t²y'' - 4ty' + 6y = 0 is

y₁(t) = t²

Using the method of reduction of order, let us assume, y₂(t) = v(t)y₁(t) is a solution to t²y'' - 4ty' + 6y = 0 for suitable choice of v(t). So,

y₂ = vt²

y₂' = 2vt + t²v'

y₂'' = 2v + 2tv' + 2tv' + t²v''

y₂'' = 2v + 4tv' + t²v''

Substituting this

t²×( 2v + 4tv' + t²v'') - 4t×(2vt + t²v') + 6×(vt²) = 0

t⁴v'' = 0

v'' = 0

v' = c, c is a constant

v = ct

Therefore, y₂(t) = ct×t²

y₂ (t) = ct³

Therefore general solution will be y(t) = c₁t² + c₂t³

To know more on second order differential equation

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Related Questions

Can some please help me?
First person gets Brainliest, 10 points!

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Answer:

oof iiiiiimmmmmmmmmso sorrry

To find area, you do length * width
For the rectangle, the length is 48 inches and the width is 32 inches.
To find the area of the rectangle, we do 48 * 32
48 * 32 = 1,536
The area of the rectangle is 1,536 inches.
To find the area of a triangle, it is a little different.
To find the area of a triangle, you use the following formula: A = 1/2 bh
We use 48 inches for the base of the triangle since the base side is equivalent to the base side of the rectangle, which is 48. We use 12 inches for the height.
In this case, we do: Area = 1/2(48)(12)
Using PEMDAS, we do multiplication or division depending on which one comes first.
In this case, division comes first
1/2(48) or 48/2 = 24
Then multiply
24 * 12 = 288
The area of the triangle is 288 inches.

PLEASE HELP WILL MARK BRAINLIST AND GIVE EXTRA 5 POINTS ​

Answers

Answer:

Danny does

Step-by-step explanation:

Compare the fraction of seconds, find their common denominator, then compare the nominators.

3/12, 4/12

Danny's fraction has the least nonimanator so Danny ate the fastest.

Please help me!
No links!!! Please!

Answers

Answer:

d = -3

Step-by-step explanation:

-3 -9 = -12

-12/6

= -2

Please someone help, I know its kind of a lot, but I need these answers fast pls.
Using the graphing calculator, type in the table and complete a linear regression. The value of the correlation coefficient is found next to the letter (__) in the table. The value of the correlation coefficient is (__) [round to the hundredths place]. When the correlation coefficient is interpreted, it means that the correlation is (__) and (__). This means the points will be (__) [close or further away] to the line.

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Answer:

Im not sure

Step-by-step explanation:

GOOD LOOK ON YOUR TEST HE DISCONN-ECTED

What is the concept of cause and effect?
A.
when an action causes something to come into effect
B.
when an action is caused but there is no resulting effect
C.
when an action doesn't actually have a resulting effect
D.
when an action leads to an effect that is not desired

Answers

Answer:

A.  when an action causes something to come into effect

Step-by-step explanation:

Mark as brainliest please. Hope the answer helps :)

In ΔVWX, v = 5.4 cm, x = 5.9 cm and ∠X=64°. Find all possible values of ∠V, to the nearest 10th of a degree.

Answers

Answer:

34

Step-by-step explanation:

Answer:55.3

Step-by-step explanation:

Does any body know how to find Late Payment in Mathematics.​

Answers

Answer:

I don't believe there is a standard formula for late payments. The late payment charge would vary by the lending institution. Some may have their own formula and some may have a set charge.

Step-by-step explanation:

What's the plura form l of
[tex] \huge\mathfrak\pink{formula} \ [/tex]
​

Answers

I believe that the answer is formulae

George bought a model of a Viking ship for $68. If he paid
$5.10 in sales tax, what was the sales tax rate?

Answers

Answer:

We can convert 6.75% to a decimal by dividing by 100.

If x is the price of the house, then the sales tax is 0.0675x. The price of the house and the sales tax add up to $319,000.

x+0.0675x=319,000

Combe terms on the left.

1.0675x=319,000

Finally, divide both sides by 1.0675.

x=319,0001.0675=298,829.04

10 seconds : 1 minute as a fraction in simplest form

Answers

Answer:

1/6

Step-by-step explanation:

60 seconds is one minute, so 10 seconds is one-sixth of a minute.

Answer:

Was there supposed to be an attachment?

Step-by-step explanation:

I think there was supposed to be an object but um, i will try my best with the info there is.

10 seconds in a fraction of a whole minute is 1/6. (10/60 = 1/6)

1 minute as a fraction is just (60/60 or 1)

PLEASE HELP NO LINKS IM TIMED

Answers

it is c bc u divide and then it will be alone it is c

Answer:

3: multiply by -2

6: y= 2 2/9

Hope this helped!

Use the distributive property to factor the expression below.
544 y - 12 x 7

Answers

The answer is 4 (136y-21)

Explanation:

Factor 4 out of 544y.
4 (136y) - 12*7

Factor 4 out of -12*7.
4 (136y) + 4 (-3*7)

Factor 4 out of 4.
(136y) + 4 (-3*7)
4 (136y- 3*7)

Multiply -3 by 7.
4 (136y - 21)

3. Label all the following values: You may label the graph or write the approximate values. A. Median = 7 B. Lower quartile (Q1) C. Upper quartile (Q3) D. Minimum E. Maximum

Answers

Answer:

is this a equation for HW for is this random?

Step-by-step explanation:

hi pls answer <333333

Answers

Answer:

6 , -6 , -9 , 9

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

Answer:

mom

Step-by-step explanation:

1/2 x 1 3/5 to the simplest form

Answers

Answer:

4/5

Step-by-step explanation:

Convert 1 3/5 into improper fraction

1 3/5 -> 8/5

1/2x8/5= 8/10

8/10= 4/5

what is a name for the marked angle​

Answers

Answer:

You can name a specific angle by using the vertex point, and a point on each of the angle's rays. The name of the angle is simply the three letters representing those points, with the vertex point listed in the middle. You can also name angles by looking at their size.

What transformation of Figure 1 results in Figure 2.? Select from the drop-down menu to correctly complete the statement. A Choose... of Figure 1 results in Figure 2. Figure 2 is a triangle and it is a transformation of Figure 1

Answers

Answer:

fliped up ward

Step-by-step explanation:

Answer:

a rotation,

Step-by-step explanation:

just took the quiz

PLEASE PLEASE HELP IVE BEEN STUCK ON THIS FOR TOO LONG

Answers

Answer:

10

Step-by-step explanation:

Answer: 10

Steps:
((hk - 4)/2) + 6 =
(-4*-3)-4/2) + 6 =
(12-4/2) + 6 =
(8/2) + 6 =
4 + 6 = 10

Rewrite 2.7 ÷ 0.3 as a fraction.

Answers

Answer:

the answer is 9

check the picture for workings

Mhanifa can you please help? I will mark brainliest! This is due soon!

Answers

Answer:

In a n -sided polygon, sum of its interior angles is (n−2)×180∘ , hence sum of the interior angles in a convex hexagon is (6−2)×180∘=720∘ .

Answer:

Q1

Sum of interior angles on n-sides polygon is:

S = (n - 2)*180°

Sum of interior angles of a hexagon (6-sided polygon):

S = (6 - 2)*180° = 4*180° = 720°Q9

Sum of exterior angles of any polygon is 360°

Each exterior angle of a pentagon is:

360°/5 = 72°

luisa is building a sand box in her backyard. she places four pieces of wood in a rectangle to form the frame. the rectangle is 4 feet long and 3 feet wide. how can she use a measuring tape to make sure that the corners of the frame will be right angles?

Answers

Answer:

As we know rectangles have 90 degree angles at all 4 of its corners.

In this question we know that the length is 4 feet while the bredth is 3 feet.

Therefore to solve this answer we can use the Pythagoras theorm.

By Pythagoras:

[tex]4^{2} + 3^{2} = diagonal^{2}[/tex]

Therefore the diagonal must be 5 feet

So if Luisa measures the diagonal with a tape and it measures 5

Then it proves that all 4 corners due have 90 degree angles

Please do mark my answer as brainliest. It would really help me answer more of such questions in the future :)

What is the measure of arc QSR?

Answers

Answer:

i need a picture for this problem.

Step-by-step explanation:

Answer:

250°

Step-by-step explanation:

Got it right on edge

Which choice is similar to the figure shown?

Please help I’m confused on what to do.

Answers

The top left figure is similar with the figure given in this problem.

What are similar figures?

Two figures are defined as similar triangles when they share these two features listed as follows:

Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.

Hence the top left figure is similar with the figure given in this problem, as:

5/2 = 20/8.The angle measures are the same.

More can be learned about similar figures at brainly.com/question/14285697

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Write an equation for slope -4 y- intercept0

Answers

Answer:

Step-by-step explanation:

If the slope of this line is -4 and the y-intercept is 0, then we can write the slope-intercept equation for this line as

y = -4x + 0, or just y = -4x

PLZ HELP ASAP WILL GIVE BRAINLIEST IF CORRECT The figure shows the letter Z and four of its transformed images-A, B, C, and D:

Which of the four images was formed by a reflection of the letter Z?
(4 points)

A
B
C
D

Answers

Answer:

kjsdhkjb

Step-by-step explanation:

Answer is a.

15 divided by 8.145 no need to explain

Answers

Answer:

1.841621

Step-by-step explanation:

15÷8.145

1.841621

1.84162063 is the answer

Observa los puntajes de las respuestas de una evaluación que tuvo de 100 preguntas. Si Alfredo contestó correctamente 57 preguntas, 16 incorrectas y el resto las dejó en blanco, ¿qué puntuación obtuvo en la evaluación?

Answers

La pregunta está incompleta:

Observa los puntajes de las respuestas de una evaluación que tuvo de 100 preguntas. Si Alfredo contestó correctamente 57 preguntas, 16 incorrectas y el resto las dejó en blanco, ¿qué puntuación obtuvo en la evaluación?

Puntos por respuesta:

Correctas: 4

En blanco: -1

Incorrectas: -3

Answer:

Alfredo obtuvo una puntuación de 153.

Step-by-step explanation:

De acuerdo a la información proporcionada, conoces el número de preguntas en la evaluación y el número de preguntas que Alfredo contestó de forma correcta e incorrecta y tienes que restar estas del total de preguntas para encontrar el número de preguntas que dejó en blanco:

100-57-16=27

Ahora, debes multiplicar el número de respuestas correctas, incorrectas y en blanco por su respectivo puntaje:

Correctas: 57*4=228

En blanco: 27*(-1)=-27

Incorrectas: 16*(-3)=-48

Finalmente, debes sumar los resultados obtenidos por cada tipo de respuesta:

228+(-27)+(-48)= 228-27-48=153

De acuerdo a esto, la respuesta es que Alfredo obtuvo una puntuación de 153.

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Answers

Answer:

B

Step-by-step explanation:

Answer:

Thats a tuff 1 A estimate of B

Step-by-step explanation:

Find the opposite of the opposite of each integer.
5. -4
7. 8
6. -15
8. -7

Answers

Answer:

5: 4

7: -8

6: 15

8: 7

I hope this helps you <3

Step-by-step explanation:

PLEASE HELP MEEE!!!!!

Answers

answer is A 400 x .45 is 180 plus 25 = 205
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