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## Homework Statement

Fnet = F

_{friction}+ F

_{airresistance}= μmg + cv

^{2}= ma

Essentially I just need to get this in a v(x) form. Prof said that we need to go about it by doing this:

F = m[itex]\ddot{x}[/itex] = m [itex]\dot{x}[/itex] * d[itex]\dot{x}[/itex]/dx

and then integrating to get v(x)

## The Attempt at a Solution

so...

μmg + cv

^{2}= m [itex]\dot{x}[/itex] * d[itex]\dot{x}[/itex]/dx

And this is where I just can't figure it out. I'm terrible with DEs.

I thought of moving the 1/dx to the other side and then integrating both sides, but I get stuck, especially since v

^{2}can be written as [itex]\dot{x}[/itex]

^{2}, right? And that messes with my sleep-deprived brain a little, lol. Any nudge in the right direction would be greatly appreciated!