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Illusion [34]
3 years ago
7

1) Use power series to find the series solution to the differential equation y'+2y = 0 PLEASE SHOW ALL YOUR WORK, OR RISK LOSING

ALL POINTS!!
Mathematics
1 answer:
iogann1982 [59]3 years ago
7 0

If

y=\displaystyle\sum_{n=0}^\infty a_nx^n

then

y'=\displaystyle\sum_{n=1}^\infty na_nx^{n-1}=\sum_{n=0}^\infty(n+1)a_{n+1}x^n

The ODE in terms of these series is

\displaystyle\sum_{n=0}^\infty(n+1)a_{n+1}x^n+2\sum_{n=0}^\infty a_nx^n=0

\displaystyle\sum_{n=0}^\infty\bigg(a_{n+1}+2a_n\bigg)x^n=0

\implies\begin{cases}a_0=y(0)\\(n+1)a_{n+1}=-2a_n&\text{for }n\ge0\end{cases}

We can solve the recurrence exactly by substitution:

a_{n+1}=-\dfrac2{n+1}a_n=\dfrac{2^2}{(n+1)n}a_{n-1}=-\dfrac{2^3}{(n+1)n(n-1)}a_{n-2}=\cdots=\dfrac{(-2)^{n+1}}{(n+1)!}a_0

\implies a_n=\dfrac{(-2)^n}{n!}a_0

So the ODE has solution

y(x)=\displaystyle a_0\sum_{n=0}^\infty\frac{(-2x)^n}{n!}

which you may recognize as the power series of the exponential function. Then

\boxed{y(x)=a_0e^{-2x}}

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The triangles are congruent. Write the<br><br>congruence statement (LT#4)
gogolik [260]

Answer:

C

Step-by-step explanation:

Look at the angle markings. Angle C has one mark, Angles E and S have two marks, and Angles D and R have three marks.

Therefore, these angles correspond with one another and determine the order of the letters.

8 0
3 years ago
I need help please help me thanks
Nady [450]

Answer:

1. The y-intercept 8 means you start off with $8. The slope 1/4 means how much money you have to pay for the amount of tickets purchased for carnival games.

2. The y-intercept 2 means the number of chapters you started reading and the slope 5/4 means the number of chapters you read per day.

3. The y-intercept 3 means the inital (start) cost of a muffin delivery and the slope 2 means the cost of each muffin delivery for the number of muffins you ordered.

Number 3 on the slope part might be the other way around if I'm wrong :)

7 0
3 years ago
6. Which expression is equivalent to -21 + 28x?
Rina8888 [55]
Solution,
-28x^2+35x
take the common,
-7x(4x-5)
The answer is -7x(4x-5)
Here,
If we solve,
-7x(4x-5)
Then, the answer would be:
= -7x*4x+7x*5
= -28x^2+35x
Hope it helps
Good luck on your assignment
3 0
3 years ago
ISTEP IS COMING UP AND IM NOT READY!!!
AlekseyPX

> and < with the lines under it mean that they can also be equal to the constant on the other side (greater/less than or equal to)

So x <= 3 can be anything less than 3 and 3.

*the = in this inequality is the equivalent of a line

Now vice versa.

x => 3 can be anything greater than 3 and 3.

Now for the dots.

The open dots in signs are (< and >).

Basically they start at that point they are on but don't include it.

So an open dot at 3 pointing to the left means that the value is greater than 3 but does not include 3.

The closed dots in signs are (<= and =>).

They start at the point and include it.

So a closed dot a 3 pointing to the left means that the value is greater than 3 and includes 3.

Arrows.

Arrows pointing to the left mean that the values are getting bigger.

Arrows pointing to the right mean that the values are getting smaller.

ie : An arrow pointing to the left with a starting point at 3 = 3 and anything bigger, such as 4.

ie : An arrow pointing to the right with a starting point at 3 = 3 and anything smaller, such as 2.

Solve for problems.

The main concept is isolate the variable.

This basically means make the variable be lonely ^^

Use +, -, *, and /

Ex : 6x + 2 > 3

First, we would subtract 2 from both sides.

6x > 1

Then, we would divide each side by 6, leaving the x alone.

x > 1/6

And voila! x is anything greater than 1/6 but it does not include 1/6.

Hope this helps! ^^

8 0
3 years ago
Read 2 more answers
Identify true statements. You must select all that apply.
Maksim231197 [3]

Answer:

c in any set of ordered pairs,the second coordinate is called domain

Step-by-step explanation:

plato user only

7 0
2 years ago
Read 2 more answers
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