Solve dv/dt=-bv/m-g

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

Solve for b

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

Steps for Solving Linear Equation

Multiply both sides of the equation by m.

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

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

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

Add gm to both sides.

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

The equation is in standard form.

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

Divide both sides by -v.

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

Dividing by -v undoes the multiplication by -v.

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

Divide gm by -v.

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

Solve for g

$$g=-\frac{bv}{m}$$

$$m\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by m.

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

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

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

Add bv to both sides.

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

The equation is in standard form.

$$\left(-m\right)g=bv$$

Divide both sides by -m.

$$\frac{\left(-m\right)g}{-m}=\frac{bv}{-m}$$

Dividing by -m undoes the multiplication by -m.

$$g=\frac{bv}{-m}$$

Divide bv by -m.

$$g=-\frac{bv}{m}$$