Where is the best place to put the arbitrary constant?

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The discussion centers on the placement of arbitrary constants when solving first-order differential equations. The integration step is crucial, as the constant, typically denoted as C, can be added after integrating the equation with respect to a variable, such as x. The choice of constant, whether C, -C, or 100*C, does not affect the solution's validity since it will vanish upon differentiation. Clarity in terminology is essential for understanding the integration process and the role of constants.

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funlord
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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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"Left side" and "right side" doesn't really mean anything. Do you have a particular example in which this is causing you confusion?
 
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 ?
 

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