# me Split this Equation into 2 equations

• memarf1
In summary, you are trying to turn equations into separate equations to be able to place them in a runge kutta problem. You propose that equations 1 and 2 have the following conditions:-f (x) = A\cos x + B\sin x-f ' (x) = -A\sin x + B\cos xHowever, before you can translate the equations, you mention that the conditions are very confusing. You suggest sticking to the format \frac{d^{2}y}{dx^{2}} or y''yes, that is correct. This helps to organize the equations. Next, you mention that you have another post with your C++ code, but the code is

#### memarf1

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??

Last edited:
memarf1 said:
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:

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:

$$\frac{d''f}{dx''} + f = 0$$

Therefore:

$$f (x) = A\cos x + B\sin x$$
$$f ' (x) = -A\sin x + B\cos x$$
$$f '' (x) = -A\cos x - B\sin x$$

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

$$\frac{d''f}{dx''}$$

Please stick to something like this:

$$\frac{d^{2}y}{dx^{2}} \quad \text{or} \quad y''$$

yes, that is correct.

Off Subject, but what is latex?

memarf1 said:
yes, that is correct.

Off Subject, but what is latex?

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.

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.

## 1. What does "Split this Equation into 2 equations" mean?

"Splitting" an equation means separating it into two separate equations. This is often done when an equation is too complex or has too many variables to be easily solved as one equation.

## 2. How do I know when to split an equation into 2 equations?

You may want to consider splitting an equation if it contains multiple variables and you are having trouble solving for a specific variable or if the equation is very long and complicated.

## 3. What are the benefits of splitting an equation into 2 equations?

Splitting an equation can make it easier to solve by breaking it down into smaller, more manageable parts. It can also help to isolate specific variables and make the overall problem easier to understand.

## 4. Is it always necessary to split an equation into 2 equations?

No, it is not always necessary to split an equation into 2 equations. In some cases, the equation may be simple enough to solve as one equation or there may be other methods to solve it without splitting.

## 5. What are some tips for effectively splitting an equation into 2 equations?

One tip is to start by identifying any terms or variables that can be isolated or simplified on their own. Then, create two separate equations using these simplified terms and continue solving from there. It may also be helpful to use substitution or elimination methods to connect the two equations together.