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2 years ago

Which table has a constant al proportionality between y and 1.57 Choose 1 answer

Mathematics

1 answer:

Blizzard [7]2 years ago

8 0

Answer:

Step-by-step explanation:

I did this problem before

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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

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

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1 year ago

1. The sales tax in New York is 8.25%. How much will an $83.99 jacket cost, including sales tax?

konstantin123 [22]

1.) $83.99 * 0.0825= $6.929175 round that to $6.93 add $83.99 +6.93=$90.92

2). $349.65 divided by 7 = $49.95 for each tree

3)V=l*w*h 13*11*16= 2288 cubic feet

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2 years ago

Which two polygons is this polygon subdivided into?

marysya [2.9K]

Answer:

no diagram

Step-by-step explanation:

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Write the equation of the line shown in the graph. Please help.

jeka57 [31]

Answer:

y = 3

Step-by-step explanation:

The y-coordinate of all points on the graph is 3.

The equation is y = 3

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2 years ago

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In AHIJ, h = 38 inches, i = 45 inches and j=61 inches. Find the measure of ZH to the nearest degree.

Paraphin [41]

Answer:

38°

Step-by-step explanation:

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2 years ago

Which table has a constant al proportionality between y and 1.57 Choose 1 answer​

Which table has a constant al proportionality between y and 1.57 Choose 1 answer