Mathematics, 03.07.2020 18:01 KayPink5723

The indicated function y1(x) is a solution of the associated homogeneous equation. Use the method of reduction of order to find a second solution y2(x) of the homogeneous equation and a particular solution yp(x) of the given nonhomogeneous equation. y''-25y= 4; y1=e^-5x

a. y2(x) = ?
b. yp(x) = ?

Answers: 1

Show answers

Answers

Answer from: lilisncz

a) y₂ (x) = e ⁵ˣ

Complementary function

$y_{C} = C_{1} {e^{-5x} } + C_{2} {e^{5x} }$

b) particular integral

$P.I = y_{p} = \frac{-4}{25}$

Step-by-step explanation:

step(i):-

Given differential equation y''-25y= 4

operator form

⇒ D²y - 25 y =4

⇒ (D² - 25) y =4

This is the form of f(D)y = ∝(x)

where f(m) = D² - 25 and ∝(x) =4

The auxiliary equation A(m) =0

⇒ m² - 25 =0

m² - 5² =0

⇒ (m+5)(m-5) =0

⇒ m =-5 , 5

Complementary function

$y_{C} = C_{1} {e^{-5x} } + C_{2} {e^{5x} }$

This is form of

$y_{C} = C_{1} y_{1} (x) + C_{2} y_{2} (x)$

where y₁ (x) = e⁻⁵ˣ and y₂ (x) = e ⁵ˣ

Step(ii):-

Particular integral:-

$P.I = y_{p} = \frac{1}{f(D)} \alpha (x)$

$P.I = y_{p} = \frac{1}{D^{2} -25} 4$

= $= \frac{1}{D^{2} -25} 4e^{0x}$

put D = 0

The particular integral

$y_{p} = \frac{1}{ -25} 4$

$P.I = y_{p} = \frac{-4}{25}$

Conclusion:-

General solution of given differential equation

$y = y_{C} +y_{P}$

$y = C_{1} {e^{-5x} } + C_{2} {e^{5x} } -\frac{4}{25}$

Answer from: Quest

see below

step-by-step explanation:

7. there are 10 data points in the set. the middle point is between 5 and 6. the middle point in the top half is 8 and the middle point in the bottom half is 3. to find the iqr , take point 8 and subtract point 3

mid term point 8 = 100 point 3 = 88

iqr = 100-88 = 12

final point 8 = 93 point 3 = 78

iqr = 93 - 78 = 15

the final has the greatest iqr

6. b - there is a high data value that causes the data set to be asymmetrical for the males: the data for males are high and asymmetrical . there is an outlier for the males that skews the data

5. the iqr is a better measure of spread for the movies and basketball games. since the basketball game has an outlier, we do not want to use standard deviation for measurement.

3. the exam median is much higher than the class median. the median line is farther to the right on the exams

2. there is no way to tell what the means are from the box and whisker plots.

Answer from: Quest

answer: .75 km

step-by-step explanation: