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Anon25 [30]
3 years ago
6

Write the given differential equation in the form L(y) = g(x), where L is a linear differential operator with constant coefficie

nts. If possible, factor L. (Use D for the differential operator.) y(4) + 8y' = 6
Mathematics
2 answers:
Burka [1]3 years ago
7 0

Answer:

Step-by-step explanation:

Given the differential equation

y^(4) + 8y' = 6

We want to write this in the form

L(y) = g(x)

Where L is a linear differential operator with constant coefficient.

A linear differential operator of the nth order is a linear combination of derivative operators up to n.

L = D^n + a_1D^(n-1) + a_2D^(n-2) + ... + a_n,

defined by

Ly = y^n + a_1y^(n-1) + a_2y^(n-2) + ... + a_(n-1)y' + a_ny

Where a_i are continuous functions of x.

Now, we have

y^(4) + 8y' = 6

Let d/dx = D

Then

D^4 y + 8Dy = 6

D(D³ + 8)y = 6

Consider

D(D³ + 8)y = 0

The auxiliary equation is

m(m³ + 8) = 0

m = 0

Or

m³ + 8 = 0

=> m³ = -8

=> m = -2

The complimentary solution is

y = C1 + (C2 + C3x + C4x²)e^(-2x)

The particular integral is

y_p = Ax

y' = A

y'' = y''' = y^(4) = 0

Using these

0 + 8A = 6

A = 6/8 = 3/4

So

y = C1 + (C2 + C3x + C4x²)e^(-2x) + 3/4

Greeley [361]3 years ago
5 0

Answer:

The differential equation will be like the one shown below

Step-by-step explanation:

Data:

Let the equation be given as:

y(4) + 8y' = 6

The equation will be expressed linearly as follows:

y(4) + 8\frac{dy}{dx}  = 6

8\frac{dy}{dx}+ 4y = 6

This is the linear form of the differential equation.

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2 years ago
Through a regular hexagon whose base edge is 8cm and whose height ii 12cma hole in the shape of the right prism with ots end bei
guapka [62]

The total surface area of the remaining solid is 48(4+✓3) centimeters square.

<h3>How to calculate the surface area?</h3>

Through a regular hexagonal prism whose base edge is 8 cm and the height is 12 cm, a hole in the shape of a right prism.

The formula for the total surface area will be:

= Total surface area=2(area of the base)+ parameter of base × height

where,

Height= 8cm

Parameter of base=12(2) = 24

Area of the base= 6×✓3/4×4² = 64✓3/4

The surface area of the remaining solid will be:

= 2(64✓3/4) + 24 × 8

= 2(64✓3/4 + 192

With the hole is a rhombus prism with the following parameters:

diagonal 1 = 6, diagonal 2 = 8, height = 12

The volume is:

V1 =0.5 × d1 × d2 × h

V1 = 0.5 × 6 × 8 × 12

V1 = 96

The dimensions of the hexagonal prism are:

Base edge (a) = 8

Height (h) = 12

The volume is

V2 = (3✓(3)/2)a²h

V2 = (3✓3)/2) × 8² × 12

V2 = 1152✓3

The remaining volume is

V = V2 -V1

V = 1152✓3 - 96

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brainly.com/question/27127032

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2 years ago
In the third degree polynomial function f(x) =x^3 + 4x, why are 2i and -2i zeros?
IgorC [24]

Answer:

We just need to evaluate and get f(2i)=0, f(-2i)=0.

Step-by-step explanation:

Since i^2=-1, then i^3=i^2i=-i, and we can apply this when we evaluate f(x) =x^3 + 4x for 2i and -2i.

First we have:

f(2i) =(2i)^3 + 4(2i)=2^3i^3+8i=8(-i)+8i=0

Which shows that 2i is a zero of f(x).

Then we have:

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Which shows that -2i is a zero of f(x).

4 0
3 years ago
19. answer this question.​
Irina-Kira [14]
<h3>♫ - - - - - - - - - - - - - - - ~<u>Hello There</u>!~ - - - - - - - - - - - - - - - ♫</h3>

➷ final = original x multiplier^n

n is the number of years

Substitute the values in:

final = 3800 x 1.054^3

final = 4449.440763

The closest answer is A

<h3><u>✽</u></h3>

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

5 0
3 years ago
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