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2 years ago

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Find the general solution of the given differential equation. x2y' + xy = 8 y(x) = give the largest interval over which the gene

ral solution is defined. (think about the implications of any singular points. enter your answer using interval notation.) determine whether there are any transient terms in the general solution. (enter the transient terms as a comma-separated list; if there are none, enter none.)

1 answer:

topjm [15]2 years ago

5 0

$x^2y'+xy=8$
$xy'+y=\dfrac8x$
$(xy)'=\dfrac8x\implies xy=8\ln|x|+C\implies y=\dfrac{8\ln|x|}x+\dfrac Cx$

which wouldn't be a valid solution over any interval containing $x=0$ .

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What is the nth term of the sequence -2 -8 -18 -32 -50

andreev551 [17]

Answer:

-2n²

Step-by-step explanation:

Using the image attached:
We see that the second differences (blue ones) are all equal so we conclude that this is a quadratic sequence.
The quadratic sequence has the form:
$T_{n} = an^{2} +bn +c$

To find the value of a we just divide second difference ( -4 ) by 2:

$a = \frac{-4}{2}= -2$

Now we have:

$T_{n}= -2n^{2} +bn+c$

Substitute $n_{1}$ and $n_{2}$ into the equation above:

$T_{1} = -2(1)^{2} +b(1) +c$

$T_{2} = -2(2)^{2} +b(2)+c$

Since $T_{1}$ = -2 and $T_{2}$ = -8 , after simplification we have:

$b +c =0$
$2b+c=0$

The solution of this system is:

b=0, c =0

The general term is :

$T_{n} = -2n^{2}$

6 0

1 year ago

A man has 14 coins in his pocket, all of which are dimes and quarters. If the total value of his

S_A_V [24]

Answer:

9 quarters 5 dimes!

Step-by-step explanation:

9x0.25=2.25

5x0.10=0.50

2.25+0.50=2.75

6 0

3 years ago

Round it to nearest fifths

Yanka [14]

Answer:

mean = $11.15

median = $11.30

mode = $9.90, $10.70, $11.90, $12.05

Step-by-step explanation:

Ordered from smallest to largest

9.89, 10.71, 11.90, 12.06

The mean is the middle number.

There are two numbers in the middle so you have to add them together and divide by 2.

(10.71 + 11.90)/2 = 11.305

rounded 11.30

Mode is the number that appears the most. All of the prices are listed once. They are all the mode.

Mean is (10.71+11.90+9.89+12.06)/4 = 11.14

round 11.15

5 0

3 years ago

Is 6/1 equivalent to 6/6

Nadusha1986 [10]

Yes, hope this helps

5 0

2 years ago

Read 2 more answers

Which angle is an x-intercept for the function y = cos(1)<br> A.0<br> B.2<br> C. £<br> D. 2£

noname [10]

Answer: C. $\pi$

=======================================================

Explanation:

The x intercept always occurs when y = 0.

Use the unit circle to determine that $\cos(\theta) = 0$ when $\theta = \frac{\pi}{2} \text{ and } \theta = \frac{3\pi}{2}$

So if $x = \pi$ , then we have

$y = \cos\left(\frac{1}{2}x\right)\\\\y = \cos\left(\frac{x}{2}\right)\\\\y = \cos\left(\frac{\pi}{2}\right)\\\\y = 0\\\\$

which shows us that $(\pi, 0)$ is the location of one of the infinitely many x intercepts for this function.

3 0

2 years ago