Please Help me Split this Equation into 2 equations

  • Thread starter memarf1
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Main Question or Discussion Point

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:

[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??
 
Last edited:

Answers and Replies

  • #2
Zurtex
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Homework Helper
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memarf1 said:
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:

d''f______________________f (x) = Acosx + Bsinx
--- + f = 0______________f ' (x) = -Asinx + Bcosx
dx''______________________f '' (x) = -Acosx - Bsinx
____df_________df
g = ----_______---- - g = 0 is identical to d''f
____dx_________dx____________________---- + f = 0
_____________________________________dx''
so
___dg
__---- + f = 0______________if f(0) = 1____and if____f(0) = 0
___dx_______________________f '(0) = 0____________g(0) = 1

My organization may be confusing, ignore long underscore lines, and some of the stuff is organized up and down instead of left and right.
any suggestions??
Right, you really need to learn Latex. So your post I tjink would go like this:

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

Therefore:

[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]

However, before I try to translate the rest, I feel it worth noting that this is very confusing:

[tex]\frac{d''f}{dx''}[/tex]

Please stick to something like this:

[tex]\frac{d^{2}y}{dx^{2}} \quad \text{or} \quad y''[/tex]
 
  • #3
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yes, that is correct.

Off Subject, but what is latex?

Please continue your help.
 
  • #4
Zurtex
Science Advisor
Homework Helper
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memarf1 said:
yes, that is correct.

Off Subject, but what is latex?

Please continue your help.
https://www.physicsforums.com/showthread.php?t=8997

Click on any of my equtions and a box should appear showing the cde I used to write it.

It's very early in the morning here, I'll come back and look at your problem later sorry, too tired right now.
 
  • #5
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Ok, well, I have changed the formatting, thank you for your continued help, ill check back in in the morning. Thanks again.

Im just looking for the 2 equations to plug into the runge kutta 4. I hope you can help. I have another post with my C++ code in it, but the code is correct. I just have to do this to show my professor.
 

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