Solve -kv+mg=mdv/dt

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

Solve for g

$$\left\{\begin{matrix}g=\frac{kv}{m}\text{, }&m\neq 0\\g\in \mathrm{R}\text{, }&\left(k=0\text{ or }v=0\right)\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract \left(-k\right)v from both sides.

$$mg=m\frac{\mathrm{d}}{\mathrm{d}t}(v)-\left(-k\right)v$$

Multiply -1 and -1 to get 1.

$$mg=m\frac{\mathrm{d}}{\mathrm{d}t}(v)+kv$$

The equation is in standard form.

$$mg=kv$$

Divide both sides by m.

$$\frac{mg}{m}=\frac{kv}{m}$$

Dividing by m undoes the multiplication by m.

$$g=\frac{kv}{m}$$

Solve for k

$$\left\{\begin{matrix}k=\frac{gm}{v}\text{, }&v\neq 0\\k\in \mathrm{R}\text{, }&\left(m=0\text{ or }g=0\right)\text{ and }v=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract mg from both sides.

$$\left(-k\right)v=m\frac{\mathrm{d}}{\mathrm{d}t}(v)-mg$$

Reorder the terms.

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

The equation is in standard form.

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

Divide both sides by -v.

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

Dividing by -v undoes the multiplication by -v.

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

Divide -gm by -v.

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