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2 years ago

Need help please some one

Mathematics

2 answers:

ella [17]2 years ago

5 0

Answer:

gforse

Step-by-step explanation: 660

liubo4ka [24]2 years ago

3 0

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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

Find the value of X

vredina [299]

Answer:

x=8

RPS = 36

Step-by-step explanation:

QPS = 180

The two angles that form QPS

QPR + RPS = 180

7x+88 + 3x+12 = 180

Combine like terms

10x+100 =180

Subtract 100 from each side

10x = 180-100

10x = 80

Divide by 10

x =80/10

x = 8

RPS = 3x+12

= 3(8)+12

24+12

7 0

3 years ago

1) Para uma estratégia de marketing de conteúdo adequada, é necessário

pentagon [3]

Answer:

hello gret person i dont know wat i amdoing i am b

8 0

3 years ago

If g(x)=11x+3 find g(x+7) and g(x)+g(7).

Liono4ka [1.6K]

Answer:

g(x + 7) = 11x + 80

g(x) + g(7) = 11x + 83

Step-by-step explanation:

g(x + 7) = 11(x + 7) + 3 = 11x + 77 + 3 = 11x + 80

g(x) + g(7) = 11x + 3 + 11(7) + 3 = 11x + 3 + 77 + 3 = 11x + 83

8 0

2 years ago

After sitting in a refrigerator for a while, a turkey at a temperature of 34 degrees F is placed on the counter and slowly warms

Anton [14]

Answer:

k = 0.006
T = 48 °F

Step-by-step explanation:

The initial temperature difference of 72 -34 = 38 °F is reduced to a difference of 72 -41 = 31 °F after 35 minutes. The exponential term in the temperature expression could have the factor ...

(31/38)^(t/35) = e^(-kt)

Taking the natural log, we find ...

(t/35)ln(31/38) = -kt

k = ln(38/31)/35 ≈ 0.00581711

To the nearest thousandth, this is ...

k ≈ 0.006

Using this in the equation for temperature, we have ...

T = 72 -38e^(-0.006t)

Filling in the desired value for t (80), we find the turkey temperature after 80 minutes to be about

T = 72 -38e^(-.006×80) = 72 -38e^-.48 ≈ 48.49

T ≈ 48 °F

The value of k is about 0.006, and the turkey temperature is about 48 °F.

4 0

2 years ago