memarf1
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Im trying to turn this equation into 2 separate equations in order to place it in a runge kutta problem. This is the proposed problem and conditions:
\frac{d^2f}{dx^2} + f = 0
allowing
f (x) = A\cos x + B\sin x
f ' (x) = -A\sin x + B\cos x
f '' (x) = -A\cos x - B\sin x
and
g = \frac{df}{dx}
meaning
\frac{df}{dx} - g = 0 which is identical to \frac{d^2f}{dx^2} + f = 0
so
\frac{dg}{dx} + f = 0
the initial conditions for equation 1 are:
f (0) = 1
f ' (0) = 0
and for equation 2 are:
f (0) = 0
g (0) = 1
I hope this formatting is more easy to read.
any suggestions??
\frac{d^2f}{dx^2} + f = 0
allowing
f (x) = A\cos x + B\sin x
f ' (x) = -A\sin x + B\cos x
f '' (x) = -A\cos x - B\sin x
and
g = \frac{df}{dx}
meaning
\frac{df}{dx} - g = 0 which is identical to \frac{d^2f}{dx^2} + f = 0
so
\frac{dg}{dx} + f = 0
the initial conditions for equation 1 are:
f (0) = 1
f ' (0) = 0
and for equation 2 are:
f (0) = 0
g (0) = 1
I hope this formatting is more easy to read.
any suggestions??
Last edited: