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3 years ago

−2x−8y=10

Mathematics

1 answer:

Vilka [71]3 years ago

4 0

Answer:

Um hahahahahhahahahahahahhaha

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Use the method of undetermined coefficients to find the general solution to the de y′′−3y′ 2y=ex e2x e−x

djverab [1.8K]

I'll assume the ODE is

$y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}$

Solve the homogeneous ODE,

$y'' - 3y' + 2y = 0$

The characteristic equation

$r^2 - 3r + 2 = (r - 1) (r - 2) = 0$

has roots at $r=1$ and $r=2$ . Then the characteristic solution is

$y = C_1 e^x + C_2 e^{2x}$

For nonhomogeneous ODE (1),

$y'' - 3y' + 2y = e^x$

consider the ansatz particular solution

$y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x$

Substituting this into (1) gives

$a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1$

For the nonhomogeneous ODE (2),

$y'' - 3y' + 2y = e^{2x}$

take the ansatz

$y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}$

Substitute (2) into the ODE to get

$b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1$

Lastly, for the nonhomogeneous ODE (3)

$y'' - 3y' + 2y = e^{-x}$

take the ansatz

$y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}$

and solve for $c$ .

$ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16$

Then the general solution to the ODE is

$\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}$

6 0

2 years ago

Please answer <br><br> Will give brainlst

VMariaS [17]

Answer:

1.true

2.false

3.true

Step-by-step explanation:

please give me a brainliest :)

4 0

3 years ago

The base of a right circular cone has a radius of 4 inches and a slant height of 9 inches. If the radius and the slant height ar

ioda

Answer:

Correct option: B -> 36

Step-by-step explanation:

The surface area of a circular cone is given by the formula:

Surface area = pi * radius * (radius + slant height)

If the inicial radius is 4 in and the slant height is 9 in, we have:

Surface area = pi * 4 * (4 + 9) = 52pi in2

The radius and the slant height are multiplied by 6, so we have:

radius = 6 * 4 = 24 in

slant height = 6 * 9 = 54 in

So the new surface area is:

New surface area = pi * 24 * (24 + 54) = 1872pi in2

The factor of the surface areas is:

New surface area / Surface area = 1872pi / 52pi = 36

Correct option: B

3 0

3 years ago

What is the slope of a line that passes through the points (-2, 3) and (4, -12)?

sergiy2304 [10]

Answer:

M(gradient) has to be found like:

$\frac{ - 12 - 3}{4 + 2} = \frac{ - 15}{6} = \frac{ - 5}{2} = - 2.5$

Answer: gradient or slope is: -2.5

7 0

3 years ago

Read 2 more answers

Help me PLEASEEEEEEEEEEEEE

tatuchka [14]

Answer:

Step-by-step explanation:

A, D and F

4 0

3 years ago