Solve mdv/dt=F-kv

$$m \frac { d v } { d t } = F - k v$$

Solve for k

$$\left\{\begin{matrix}k=\frac{F}{v}\text{, }&v\neq 0\\k\in \mathrm{R}\text{, }&F=0\text{ and }v=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$F-kv=m\frac{\mathrm{d}}{\mathrm{d}t}(v)$$

Subtract F from both sides.

$$-kv=m\frac{\mathrm{d}}{\mathrm{d}t}(v)-F$$

The equation is in standard form.

$$\left(-v\right)k=-F$$

Divide both sides by -v.

$$\frac{\left(-v\right)k}{-v}=-\frac{F}{-v}$$

Dividing by -v undoes the multiplication by -v.

$$k=-\frac{F}{-v}$$

Divide -F by -v.

$$k=\frac{F}{v}$$

Solve for F

$$F=kv$$