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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:

[tex]\frac{d^2f}{dx^2} + f = 0[/tex]

allowing

[tex]f (x) = A\cos x + B\sin x[/tex]

[tex]f ' (x) = -A\sin x + B\cos x[/tex]

[tex]f '' (x) = -A\cos x - B\sin x[/tex]

and

[tex]g = \frac{df}{dx}[/tex]

meaning

[tex]\frac{df}{dx} - g = 0[/tex] which is identical to [tex]\frac{d^2f}{dx^2} + f = 0[/tex]

so

[tex]\frac{dg}{dx} + f = 0[/tex]

the initial conditions for equation 1 are:

[tex]f (0) = 1[/tex]

[tex]f ' (0) = 0[/tex]

and for equation 2 are:

[tex]f (0) = 0[/tex]

[tex]g (0) = 1[/tex]

I hope this formatting is more easy to read.

any suggestions??

[tex]\frac{d^2f}{dx^2} + f = 0[/tex]

allowing

[tex]f (x) = A\cos x + B\sin x[/tex]

[tex]f ' (x) = -A\sin x + B\cos x[/tex]

[tex]f '' (x) = -A\cos x - B\sin x[/tex]

and

[tex]g = \frac{df}{dx}[/tex]

meaning

[tex]\frac{df}{dx} - g = 0[/tex] which is identical to [tex]\frac{d^2f}{dx^2} + f = 0[/tex]

so

[tex]\frac{dg}{dx} + f = 0[/tex]

the initial conditions for equation 1 are:

[tex]f (0) = 1[/tex]

[tex]f ' (0) = 0[/tex]

and for equation 2 are:

[tex]f (0) = 0[/tex]

[tex]g (0) = 1[/tex]

I hope this formatting is more easy to read.

any suggestions??

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