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2 years ago

What is the volume of the square pyramid ?

Mathematics

1 answer:

Oxana [17]2 years ago

7 0

Answer:

Step-by-step explanation:

The answer is 4230

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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

What is the common mutiple for 1/2 1/4 1/6 1/3 and 1/5

grin007 [14]

The common multiple for 1/2 1/4 1/6 1/3 and 1/5 would be 60:

2 x 30 = 60
3 x 20 = 60
4 x 15 = 60
5 x 12 = 60
6 x 10 = 60

5 0

3 years ago

Х+ Зу = 6<br> бx — бу = 4

Sloan [31]

Answer:

the first one is x= 6-3y or if you are going to solve with the y it will be y =2 - x/3

the second one if you are solving for x it will be x= 2/3 + y if you are solving for y it will be x = 2/3 + x

Step-by-step explanation:

hope this helps

8 0

2 years ago

Read 2 more answers

How many kilograms of tin will be required to make 250 kg of an alloy, if the alloy must contain 81% copper, 14% tin and 5% lead

uysha [10]

Answer:

Step-by-step explanation:

all are obeying a constant ratio

copper 81
tin 14⇒?
lead 5
total 100 ⇒250
?=250*14/100=35

5 0

2 years ago

Read 2 more answers

Rewrite the following equation in slope intercept form<br> 11x+17y=-3

Scilla [17]

Your answer ought to be y=-11/17x-3/17.

7 0

2 years ago