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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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    @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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    @Nir: If you want $y^{(n)}(0)$ you can just plug in your conditions to get $y^{(3)}$ and so on2011-02-28