Im trying to turn this equation into 2 seperate equations in order to place it in a runge kutta problem. This is the proposed problem and conditions:(adsbygoogle = window.adsbygoogle || []).push({});

[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??

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Please Help me Split this Equation into 2 equations

**Physics Forums | Science Articles, Homework Help, Discussion**