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Daniel [21]
3 years ago
8

5. The differential equation y 00 − xy = 0 is called Airy’s equation, and is used in physics to model the refraction of light. (

a) Assume a power series solution, and find the recurrence relation of the coefficients. [Hint: When shifting the indices, one way is to let m = n − 3, then factor out x n+1 and find an+3 in terms of an. Alternatively, you can find an+2 in terms of an−1.] (b) Show that a2 = 0. [Hint: the two series for y 00 and xy don’t “start” at the same power of x, but for any solution, each term must be zero. (Why?)] (c) Find the particular solution when y(0) = 1, y 0 (0) = 0, as well as the particular solution when y(0) = 0, y 0 (0) = 1.

Mathematics
1 answer:
storchak [24]3 years ago
4 0

Not sure why, but I wasn't able to post my solution as text, so I've written it elsewhere and am posting screenshots of it here.

In the fifth attachment, the first solution is shown above the second one.

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T-5-2t+5 simplify expression
pav-90 [236]

Answer:

-t

Step-by-step explanation:

t - 5 - 2t + 5 =

t - 5 + 5 - 2t =

t - 2t =

-t

3 0
3 years ago
Read 2 more answers
(c) Find the number of sets where all three cards are the same for exactly $0$ attributes. (d) Find the number of sets where all
Cloud [144]

C. For the first card, there are three ways to choose the number of card.

For the another, there two options, and likewise there's only 1 choice of card. So there are 3 × 2 × 1 = 6 ways that the calculation can be chosen.

Doing this for the other attributes, we get 6 × 6 × 24 × 6 ways. But the order of cards does not count in a set of card, so we divide by 3! 6 * 6 * 24 × 6 ÷ 3! = 864. It means there are 864 sets for part.

D. The cards may have the same number, color, shapess, orshading.

However, also there are 6 × 24 × 6 × 3! = 144 sets of cards, If all the colors are thesame. How ever, also there are 144 sets of cards.

If all the calculation are the same. We get the same number for shape and shadings, so there are 4 × 144 = 576 sets of cards.

what is Probability?

Probability is branches of mathematics concerning numerical descriptions of how to the likely an event is to occurs, or how to the likely it is that a proposition is true. The probability of an event is a numbers between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the events and 1 indicates certain of cards.

Learn more about Probability here

brainly.com/question/13604758

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5 0
2 years ago
Due tomorrow please help
NeX [460]
For some of these, a calculator is helpul.

The sum is 294903.

_____
This is the sum of 15 terms of a geometric sequence with first term 9 and common ratio 2. That sum is given by the formula
S_{n}=a\dfrac{r^{n}-1}{r-1}
S_{15}=9\dfrac{2^{15}-1}{2-1}=9\cdot(32768-1)=294903

7 0
3 years ago
I need to know this I don’t understand and it is last one
Len [333]

Answer:

The answer is 4x

Step-by-step explanation:

Hope this helped

4 0
3 years ago
2x+y=8<br> x+y=4<br> Where do they intersect at?
Roman55 [17]

Answer:

{ \bf{2x + y = 8 -  -  - (a)}} \\ { \bf{x + y = 4 -  -  - (b)}} \\ a - b :  \\ x = 4 \\ 4 + y = 4 \\ y = 0 \\ { \tt{they \: intersect \: at \: (4, \: 0)}}

5 0
3 years ago
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