I'll start by saying maths is not my strong point and I'm struggling to stay afloat in a college maths class that is above my ability. The current topic is ordinary differential equations and I'm unsure how to handle derivatives within the equation.
Starting with an equation:
F(t) - F<sub>air</sub> = ma
And turning it into to get the equation in terms of v:
F(t)-dv^2 = mv'
I am supposed to put this in standard format and in terms of v. Can I divide both sides by m to free the v' on the right, and then if I bring the v^2 across, how does that affect the v'? Should v' just be treated as a normal v? Or rather, does mv' equal m.v' and m.v?
Sorry if this is a very basic question. Again this maths class is well above my ability.
For full reference the question states: Obtain an ODE (in standard form) of the car's horizontal velocity by applying Newton's Second Law in the x-direction and it is of a car driving along a road being pushed along by force F(t) and being affected by wind resistance Fair which is equal to dv^2