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.
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.
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 $0$.