Where is the best place to put the arbitrary constant?

In summary, the conversation discusses the confusion around where to place an arbitrary constant when solving first-order differential equations. The concept of "left side" and "right side" is not relevant in this context. The integration step allows for the addition of a constant, such as C, -C, or 100*C, which will disappear when differentiating again.
  • #1
funlord
15
1
I am having trouble to where to put the arbitrary constant in solving order differential equations. Because sometimes when I am solving, I can't really where to put the arbitrary constant if it is either the left side or right side.

I am only at equations of order one.

Plss keep it simple stupid.
 
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  • #2
"Left side" and "right side" doesn't really mean anything. Do you have a particular example in which this is causing you confusion?
 
  • #3
Usually there is an integration step where you integrate your equation over some variable x. You can add a constant, say C, after the integration because when you differentiate again, the constant will disappear. Question:
does it matter if the constant is C, -C or 100*C ?
 

FAQ: Where is the best place to put the arbitrary constant?

1. Where is the best place to put the arbitrary constant in a mathematical equation?

The best place to put the arbitrary constant in a mathematical equation is usually at the end of the equation. This is because it is convention to write equations in a simplified form, with all constants and variables on one side and the solution on the other side.

2. Do I always need to include an arbitrary constant in my equation?

No, not all equations require an arbitrary constant. It depends on the specific equation and what values are being solved for. In some cases, the arbitrary constant may cancel out during the solving process.

3. Can I put the arbitrary constant anywhere in the equation?

No, the arbitrary constant should only be placed in locations where it makes sense mathematically. It should not be placed in the middle of a term or in a position that would alter the meaning of the equation.

4. Is there a standard notation for representing an arbitrary constant?

Yes, the most common notation for an arbitrary constant is the letter "C". However, some textbooks or equations may use different letters or symbols to represent the arbitrary constant.

5. What is the purpose of an arbitrary constant in an equation?

The purpose of an arbitrary constant is to account for any unknown or unspecified values in an equation. It allows for a more general solution that can be applied to a wider range of cases.

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