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the fucnction y(x) implement the Equation y''-xy=0.

In addition, know that y(0)=0 and y'(o)=1.

find the value of y(0)^(n), which means the value of 0 in the nth derivative.

Thanks.

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    -1 Please try to post readable questions.2011-02-28
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    Don't post your questions in the imperative mode; if you have a question, please *ask*, don't give orders. Also: while your native language is likely not English, and so the English part may be excused, you could at least make some effort in getting the mathematical notation correct and legible.2011-02-28
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    (downvote removed after Arturo's edit)2011-02-28
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    what do you mean by asking and not giving orders? you know, after a while I will eventually learn how to write all the terms correctly, but you should learn from Ross's comments in my last posts about constructive criticism.2011-02-28
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    @Nir. For politeness, you should word a post like "How does one show that this happens..." instead of "Show that this happens." The first way is viewed as asking a question, where the second way is viewed as an imperative or giving someone a required assignment.2011-02-28
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    oh, I see. Lol, it's just me copy the question itself, It doesnt mean that I refer to you with this "command", it's just like you read the ex yourself, got it? But thank you for mention that, now I know.2011-02-28
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    The new edit was removed due to a mistake, Is there a way for fixing that?2011-02-28
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    @Nir: You can rollback in the version history.2011-02-28

1 Answers 1

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Add xy to both sides (To get $y'' = xy$), and start taking derivatives. A pattern emerges.

Edit: You should get:

$y^{(3)} = y + xy'$

$y^{(4)} = 2y' + xy''$

$y^{(5)} = 3y'' + xy'''$

$y^{(6)} = 4y^{(3)} + xy^{(4)}$

$y^{(7)} = 5y^{(4)} + xy^{(5)}$

and so on...

Then, ask yourself what happens when you start evaluating each of these terms at $0$.

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    Notice that I edited my equation. I did the calculation, and then wrote it without looking at my work! It should be correct now.2011-02-28
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    Thank you so much, I'll be working on it.2011-02-28
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    ok, so no success with this. what should I do with the other data?2011-02-28
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    @Nir: If you want $y^{(n)}(0)$ you can just plug in your conditions to get $y^{(3)}$ and so on2011-02-28