Solutions of Differential Equations

rayn123x
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When it is stated that a certain formula is solution to a differential equation, what does that mean in the physical world. What is the significance of a certain formula being a solution to a differential equation?
 
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The value f subscript x gives you the slope of the line tangent to f in the x direction.

EDIT: I think. I learned this like 2 weeks ago.
 
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