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3 years ago

Just number answer 22

Mathematics

2 answers:

Darina [25.2K]3 years ago

6 0

Answer:

Step-by-step explanation:

ivann1987 [24]3 years ago

3 0

Answer:

Is a u shape graph and is (4.1) and (2.1) on the graph

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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

The 6 boys in Ms.dreyvus’ class always ran together during recess.

mr_godi [17]

Answer:

36 miles each

Step-by-step explanation:

you divide 192 by 6 = 36

hope this helps

Mark brainliest please

8 0

3 years ago

Read 2 more answers

Determine if the following triangle is a right Triangle. Write your answer, claim, as a

Reptile [31]

Answer:

Step-by-step explanation:

Check if the lengths of the sides follows the Pythagorean theorem.

9² + 12² ≟ 15²

81 + 144 ≟ 225

225 = 225

Triangle ABC is a right triangle.

7 0

3 years ago

6. Emily rides her bike with a constant speed of

qaws [65]

Answer:

42 miles

Step-by-step explanation:

If it's a constant 12 miles per hour then it would be

12 mph x 3 hours = 36

then you would add that with the 1/2 hour for

12 mph x 1/2 hours = 6

36 + 6 = 42 miles traveled

8 0

2 years ago

28 is 70% of what number?

sleet_krkn [62]

Use the equation 28/.70 and you should get your answer

7 0

3 years ago

Read 2 more answers