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MissTica
2 years ago
9

What is 50 divided by 2?

Mathematics
1 answer:
goldfiish [28.3K]2 years ago
4 0

Answer:

This is the most hardest question I have seen but I think it may probably be  25

Step-by-step explanation:

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Find two power series solutions of the given differential equation about the ordinary point x = 0. compare the series solutions
monitta
I don't know what method is referred to in "section 4.3", but I'll suppose it's reduction of order and use that to find the exact solution. Take z=y', so that z'=y'' and we're left with the ODE linear in z:

y''-y'=0\implies z'-z=0\implies z=C_1e^x\implies y=C_1e^x+C_2

Now suppose y has a power series expansion

y=\displaystyle\sum_{n\ge0}a_nx^n
\implies y'=\displaystyle\sum_{n\ge1}na_nx^{n-1}
\implies y''=\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}

Then the ODE can be written as

\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}-\sum_{n\ge1}na_nx^{n-1}=0

\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}-\sum_{n\ge2}(n-1)a_{n-1}x^{n-2}=0

\displaystyle\sum_{n\ge2}\bigg[n(n-1)a_n-(n-1)a_{n-1}\bigg]x^{n-2}=0

All the coefficients of the series vanish, and setting x=0 in the power series forms for y and y' tell us that y(0)=a_0 and y'(0)=a_1, so we get the recurrence

\begin{cases}a_0=a_0\\\\a_1=a_1\\\\a_n=\dfrac{a_{n-1}}n&\text{for }n\ge2\end{cases}

We can solve explicitly for a_n quite easily:

a_n=\dfrac{a_{n-1}}n\implies a_{n-1}=\dfrac{a_{n-2}}{n-1}\implies a_n=\dfrac{a_{n-2}}{n(n-1)}

and so on. Continuing in this way we end up with

a_n=\dfrac{a_1}{n!}

so that the solution to the ODE is

y(x)=\displaystyle\sum_{n\ge0}\dfrac{a_1}{n!}x^n=a_1+a_1x+\dfrac{a_1}2x^2+\cdots=a_1e^x

We also require the solution to satisfy y(0)=a_0, which we can do easily by adding and subtracting a constant as needed:

y(x)=a_0-a_1+a_1+\displaystyle\sum_{n\ge1}\dfrac{a_1}{n!}x^n=\underbrace{a_0-a_1}_{C_2}+\underbrace{a_1}_{C_1}\displaystyle\sum_{n\ge0}\frac{x^n}{n!}
4 0
3 years ago
Tion?<br>What is/are the given in the problem? What are you going to solve?<br>How can you do​
djverab [1.8K]

Answer:

Not enough information given. Please type the whole question out.

3 0
3 years ago
62% of what number is 186
ra1l [238]

Answer:

300

Step-by-step explanation:

Let the number be X

62/100 × X = 186

X = 186 × 100/62

X = 300

7 0
3 years ago
Read 2 more answers
Practice Problem #5 Background: The pie chart shows the approximate percentages teenagers spend doing various activities in a da
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Boom get rickety rick rolled on this guys question
3 0
3 years ago
You and your brother are reading the same novel. You want to get ahead of him in the book, so you decide to read 303030 minutes
aliina [53]

Answer:

For this case we have the following notation:

y= the number of minutes that you read

x = the number of minutes that your brother read

And we have that you decide to read 30 minutes longer than your brother, so the equation would be:

y = x+30

And for the other part of the question if x =15 we got:

y = 15+30 = 45

Step-by-step explanation:

Assuming this complete question: "You and your brother are reading the same novel. You want to get ahead of him in the book, so you decide to read 30 minutes longer than your brother reads. Write an equation for the number of minutes you read, y, when your brother reads x number of minutes.

How many minutes will you read if your brother reads for 15 minutes?"

Solution to the problem

For this case we have the following notation:

y= the number of minutes that you read

x = the number of minutes that your brother read

And we have that you decide to read 30 minutes longer than your brother, so the equation would be:

y = x+30

And for the other part of the question if x =15 we got:

y = 15+30 = 45

5 0
3 years ago
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