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3 years ago

Please help me out thank you.

Mathematics

1 answer:

frozen [14]3 years ago

6 0

Answer:

A'-4

Step-by-step explanation:

why does it turn 90

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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

Which counterexample shows that the conjecture "Every parallelogram is also a rectangle" is false?

saveliy_v [14]

A parallelogram without four right angles would prove that to be false.

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3 years ago

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A rectangular floor measures 10 1/8 feet by 13 3/4 feet. If Emily buys 150 square feet of carpet, will she have enough carpet to

miss Akunina [59]

Yes she will have enough. Here is why.

10 1/8 x 13 3/4 = 139

Therefore the room is 139 square feet. She has 150 square feet of carpet, so she has enough.

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3 years ago

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3/4g=−12<br><br><br> Help me plz

anzhelika [568]

Answer:

g=-16

Step-by-step explanation:

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If lori can make 2 birdhouses in 3 hours how long will it take her to make 10 birdhouses

andrew11 [14]

Answer:

15 Hours

Step-by-step explanation:

It takes 1.5 hours to build 1 birdhouse, so multiply 1.5×10 and you get 15 hours.

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