Solutions of Differential Equations

[rayn123x]

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?

 

[AnthonyLiardo]

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.