DEs - Constants in Exercises: Why Not in General Forms?

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SUMMARY

The discussion focuses on the presence of constants in ordinary differential equations (ODEs) and their absence in general forms. Constants, such as the arbitrary constant C in the solution of the equation ##\frac {dy}{dx} = 2##, are not included in general forms because they are considered trivial to solve. The solutions represent a family of lines with a consistent slope but varying y-intercepts, illustrating that constants do contribute to the solution's generality without altering the fundamental structure of the equation.

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Students and educators in mathematics, particularly those studying differential equations, as well as anyone seeking to deepen their understanding of ODEs and the significance of constants in mathematical solutions.

Admiralibr123
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I have just started out with ODE's and in none of the general form in the classification have I seen a term with no variable but some questions do have constants in the exercise. I am just confused as to why are they not in general forms. Are they redundant? Do they not contribute anything to the solution?
 
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An example of what you mean would be helpful. Otherwise it's almost impossible to understand what you are talking about.
 
Admiralibr123 said:
I have just started out with ODE's and in none of the general form in the classification have I seen a term with no variable but some questions do have constants in the exercise. I am just confused as to why are they not in general forms. Are they redundant? Do they not contribute anything to the solution?
If I understand what you're asking, they wouldn't be in some list of general formulas because they are trivial to solve.
Here's an example: ##\frac {dy}{dx} = 2##
Solution: y = 2x + C, where C is an arbitrary constant. The solutions are a family of lines with slope 2, but with different y intercepts.

If this isn't what you're asking about, please be more specific in your question.
 

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