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STALIN [3.7K]
3 years ago
5

(a) By inspection, find a particular solution of y'' + 2y = 14. yp(x) = (b) By inspection, find a particular solution of y'' + 2

y = −8x. yp(x) = (c) Find a particular solution of y'' + 2y = −8x + 14. yp(x) = (d) Find a particular solution of y'' + 2y = 16x + 7. yp(x) =
Mathematics
1 answer:
SOVA2 [1]3 years ago
8 0

Answer:

(a) The particular solution, y_p is 7

(b) y_p is -4x

(c) y_p is -4x + 7

(d) y_p is 8x + (7/2)

Step-by-step explanation:

To find a particular solution to a differential equation by inspection - is to assume a trial function that looks like the nonhomogeneous part of the differential equation.

(a) Given y'' + 2y = 14.

Because the nonhomogeneus part of the differential equation, 14 is a constant, our trial function will be a constant too.

Let A be our trial function:

We need our trial differential equation y''_p + 2y_p = 14

Now, we differentiate y_p = A twice, to obtain y'_p and y''_p that will be substituted into the differential equation.

y'_p = 0

y''_p = 0

Substitution into the trial differential equation, we have.

0 + 2A = 14

A = 6/2 = 7

Therefore, the particular solution, y_p = A is 7

(b) y'' + 2y = −8x

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = -8x

2Ax + 2B = -8x

By inspection,

2B = 0 => B = 0

2A = -8 => A = -8/2 = -4

The particular solution y_p = Ax + B

is -4x

(c) y'' + 2y = −8x + 14

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = -8x + 14

2Ax + 2B = -8x + 14

By inspection,

2B = 14 => B = 14/2 = 7

2A = -8 => A = -8/2 = -4

The particular solution y_p = Ax + B

is -4x + 7

(d) Find a particular solution of y'' + 2y = 16x + 7

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = 16x + 7

2Ax + 2B = 16x + 7

By inspection,

2B = 7 => B = 7/2

2A = 16 => A = 16/2 = 8

The particular solution y_p = Ax + B

is 8x + (7/2)

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Answer:

24 cm²

Step-by-step explanation:

Z zadanego powyżej pytania uzyskano następujące dane:

Obwód (obwód) = 32 cm

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Obszar rombu (A) =?

Następnie określimy długość boku rombu. Można to uzyskać w następujący sposób:

Obwód, czyli obwód (P) = 32 cm

Strona (y) =?

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Podziel obie strony przez 4

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Na koniec określimy obszar rombu w następujący sposób:

Długość boków = 8 cm

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Dlatego obszar rombu jest

24 cm².

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3 years ago
What is 1/10th of 2,871,000?
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This is fairly simple. Divide 2,871,000 by 10 and that's your answer!

\frac{2,871,000}{10} =287,100

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Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 20. Find the prob
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Answer:

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Step-by-step explanation:

It is given that, it is normal distribution with mean 100 and SD as 20.

So, let's use the formula of z-score

z=\frac{x-mean}{SD}

For this problem,

x= 136

Plug in this value into the formula

z-score=\frac{136-100}{20}

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Now, use z-score table to find the probability

Find the corresponding value for the row 1.8 and the column 0.00, we do get 0.9641

So, Randomly selected adult has an IQ less than 136 is 0.9641

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Step-by-step explanation:

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