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expeople1 [14]
3 years ago
8

SELECT 3 OPTIONS:

Mathematics
1 answer:
Umnica [9.8K]3 years ago
6 0
It’s a positive slope, constant slope, and increasing function. Because it’s a straight line going diagonally to the top right, you know the slope is positive, constant, and the function is positive.
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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
1 year ago
Jill has an old bike. her parents gave her 40$ to repair it new tires is 21$ she also wants to buy a bell 5$ and a basket 13$ ho
dimaraw [331]

Answer:

She will have 1$ left

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions:
fredd [130]
Oooo ok
I don’t now true this or no
But answer is 13
7 0
3 years ago
The American flag is customarily made with its width and length in the ratio of 10 to 19. Which of the following dimensions is i
saul85 [17]
You have not provided the options, therefore, I cannot give an exact answer. However, I can help you with the procedures.

We are given that the ratio between the width and the length of the flag is 10 to 19.
This means that:
\frac{width}{length} =  \frac{10}{19}

Therefore, to get the correct choice, all you have to do is divide the width by the length, if the result is 10/19, then the dimensions given are correct.

Examples:
For length = 190 and width = 100,
width / length = 100 / 190 = 10 / 19 .........> correct choice

For length = 1.9 and width = 1,
width / length = 1 / 1.9 = 10 / 19 .......> correct choice

Hope this helps :)
3 0
3 years ago
Find area triangle of 15 ft and 18 ft<br> The area of the triangle is. Ft2
Harrizon [31]

Answer:

a= 135

Step-by-step explanation:

18*15=135

5 0
3 years ago
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