Could someone please verify if this is correct. This is the answer I am coming up with.
v(t) = 9.8m/k - (v(0)+9.8m/k)e^kt/m
I have been given an equation which is first order ODE of the velocity v(t).
v'(t) = g-(k/m)v(t)
Where g is 9.8m/s^2, k is a constant of proportionality based on the size and shape of the body falling, and m is the mass.
I am asked to find the general solution of this DE, satisfying the initial value v(o) = v0(initial velocity).
I believe that I am supposed to take g-(k/m) to be a constant. Any suggestions as to how i should go about solving this?