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Homework Statement
The differential equation that models the volume of a raindrop is [tex]\frac{dy}{dt} = kv^{2/3}[/tex] where [tex]k = 3^{2/3}(4 \pi)^{1/3}[/tex]
A) Why doesn't this equation satisfy the hypothesis of the Uniqueness Theroem?
B) Give a physical interpertation of the fact that solution to this equation with the initial condition v(0) = 0 are not unique. Does this model say anything about the way raindrops begin to form?
Homework Equations
The Attempt at a Solution
A) The equation doesn't satisfy the hypothesis Uniqueness Theroem because when v = 0, the equation's derivative does not exist.
B) At time t = 0, the raindrop does not have volume, but as t increases, it's volume increases as well.
Am I correct for both parts