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4 years ago

Peter measures the angles in a triangle.

1 answer:

4 0

Yes, it would be correct because a triangle has to add up to 180 degrees when all the angles are added up

A) Explanation:
95 + 10 + 75 = 180

B) A triangle will always add up to 180.

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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

The ordered pairs in the table below represent a linear function. x y 6 2 9 8 What is the slope of the function?

sineoko [7]

Answer:

1/2 i think :)

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

What is 9x+7y=-18 using substitution

wlad13 [49]

7y=-9x-18

that is all I can do

4 0

3 years ago

The number of games in the first round of a chess tournament is equal to 2×2×2×2×2×2. Write the number of games using an exponen

Naily [24]

Answer:

2^6

Step-by-step explanation:

2 is being multiplied 6 times meaning it would be 2 to the 6th power.

8 0

3 years ago

The graph shows the savings in Andre’s bank account.

Vadim26 [7]

Answer:

The slope is 1/5

Andre is saving 4 dollars per week.

Step-by-step explanation:

5 0

3 years ago