- #1
Dissident Dan
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Suppose that we have a function that refers to itself in its derivative or second derivitive.
For example, let's say that you have a spring for which the force is directly proportional to the distance the spring has been compressed.
F = -cx
For simplicity's sake, mass is constant, so we can just say
a = -cx
The differential-form equation for this acceleration is:
d2x/(dt)2 = -cx
And so the speed equation is
dx/dt = v0 + [inte]-cx(dt)
How would you solve this?
Or, for a simpler equation, say that the velocity of a particle depends on its position:
dx/dt = c1 + c2x
How would you solve this to get to the position function?
For example, let's say that you have a spring for which the force is directly proportional to the distance the spring has been compressed.
F = -cx
For simplicity's sake, mass is constant, so we can just say
a = -cx
The differential-form equation for this acceleration is:
d2x/(dt)2 = -cx
And so the speed equation is
dx/dt = v0 + [inte]-cx(dt)
How would you solve this?
Or, for a simpler equation, say that the velocity of a particle depends on its position:
dx/dt = c1 + c2x
How would you solve this to get to the position function?
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