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# Differential equation solution cannot describe what happens in reality

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Suppose we have a free falling object inside a planet's gravitational field with strength g.The planet's atmosphere provides a drag force which is dependant from the u^2 of the particle.

Suppose the weight of the object is m1g and the drag force due to the atmosphere is -ku^2 and lets say we set k=1 for simplicity we end up with this differential equation:

$$\frac{du}{dt} = g+\frac{u^{2}}{m_{1}}$$

and if you solve the differential equation with initial condition u(0)=0 you get

$$u(t) =\frac{\sqrt{g}}{\sqrt{m_{1}}}\cdot tan(\sqrt{g}\sqrt{m_{1}}t)$$

If I graph the function in Desmos it shows me this

However we have infinities involved and I dont think it is right.What am I missing?

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Shouldn't that be "-" in first equation? (1 comment)