Write the decimal expansion for 4/11

The indicated function y1(x) is a solution of the associated homogeneous equation. Use the method of reduction of order to find

9966 [12]

Answer:

The particular integral of given differential equation

$y_{p} = \frac{1}{4} ( x - (\frac{-5}{4} ) (1))$

General solution of given differential equation

$y = y_{c} + y_{p}$

$Y (x) = C_{1} e^{x} + C_{2} e^{4x} + \frac{1}{4} ( x + (\frac{5}{4} ))$

Step-by-step explanation:

Step(i):-

Given Differential equation y'' − 5 y' + 4 y = x

Given equation in operator form

D²y - 5 Dy + 4 y = x

⇒ ( D² - 5 D + 4 ) y =x

⇒ f(D) y = Q

where f(D) = D² - 5 D + 4 and Q(x) = x

The auxiliary equation f(m) =0

m²-5 m + 4 =0

m² - 4 m - m + 4 =0

m ( m -4 ) -1 ( m-4) =0

(m - 1) =0 and ( m-4) =0

m = 1 and m =4

The complementary function

$Y_{c} = C_{1} e^{x} + C_{2} e^{4x}$

Step(ii):-

particular integral

Particular integral

$y_{p} = \frac{1}{f(D)} Q(x) = \frac{1}{D^{2} - 5 D + 4} X$

taking common '4'

$= \frac{1}{4(1 + (\frac{D^{2} - 5 D}{4} ))} X$

$=\frac{1}{4} (1 + (\frac{D^{2} -5D}{4})^{-1} )} X$

applying binomial expression

( 1 + x )⁻¹ = 1 - x + x² - x³ +.....

$=\frac{1}{4} (1 - (\frac{D^{2} -5D}{4}) +((\frac{D^{2} -5D}{4})^{2} -...} )X$

Now simplifying and we will use notation D = $\frac{dy}{dx}$

$=\frac{1}{4} (x - (\frac{D^{2} -5D}{4})x +((\frac{D^{2} -5D}{4})^{2}(x) -...}$

Higher degree terms are neglected

$=\frac{1}{4} (x - (\frac{ -5 D}{4}) x)$

The particular integral of given differential equation

$y_{p} = \frac{1}{4} ( x - (\frac{-5}{4} ) (1))$

Final answer:-

General solution of given differential equation

$y = y_{c} + y_{p}$

$Y (x) = C_{1} e^{x} + C_{2} e^{4x} + \frac{1}{4} ( x + (\frac{5}{4} ))$

4 0

3 years ago

Plz help !!

Citrus2011 [14]

If your teacher/book requires a standard form for the equation of a line, don't forget to convert the equations into them!

6 0

3 years ago

When the outliers are removed, how does the mean change?

vagabundo [1.1K]

Answer:

The mean increases by 3.

Step-by-step explanation:

What's an outlier?

An outlier is a data point that's very different from the other data points. In this example, the outlier is 50, as the other data points are around the number 80.

What's the mean of a data set?

The mean is the average of a data set. It's found by adding up all the numbers in the set and then dividing by the number of data points there is.

How do we solve this problem?

First, we find the mean of the data set with the outlier, 50.

$\frac{50+76+78+79+79+80+81+82+82+83}{10}$
$\frac{770}{10}$
$77$

Next, we find the mean of the set without the outlier.

$\frac{76+78+79+79+80+81+82+82+83}{9}$
$\frac{720}{9}$
$80$

Lastly, we subtract 77 from 80 to find the difference.

$80 - 77 = 3$

Therefore, the answer is The mean increases by 3.

5 0

3 years ago

Divide. (5 1/4)÷(−2 1/2) Enter your answer as a mixed number, in simplest form, in the box.

FromTheMoon [43]

Answer:

4 1/5

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

En una granja se crían gallinas y conejos. Si se cuentan las cabezas son 50, si se cuentan las patas son 134. ¿Qué sistema de ec

svp [43]

Hay un total de 17 conejos y 33 gallinas

7 0

2 years ago