Solve md^2h/dt^2=-mg-mkdh/dt

$$m \frac { d ^ { 2 } h } { d t ^ { 2 } } = - m g - m k \frac { d h } { d t }$$

Solve for g

$$\left\{\begin{matrix}\\g=0\text{, }&\text{unconditionally}\\g\in \mathrm{R}\text{, }&m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\left(-m\right)g-mk\frac{\mathrm{d}(h)}{\mathrm{d}t}=m\frac{\mathrm{d}(h)}{\mathrm{d}t^{2}}$$

Add mk\frac{\mathrm{d}(h)}{\mathrm{d}t} to both sides.

$$\left(-m\right)g=m\frac{\mathrm{d}(h)}{\mathrm{d}t^{2}}+mk\frac{\mathrm{d}(h)}{\mathrm{d}t}$$

Reorder the terms.

$$-gm=m\frac{\mathrm{d}(h)}{\mathrm{d}t^{2}}+km\frac{\mathrm{d}(h)}{\mathrm{d}t}$$

The equation is in standard form.

$$\left(-m\right)g=0$$

Divide 0 by -m.

$$g=0$$

Solve for h

$$h\in \mathrm{R}$$

$$g=0\text{ or }m=0$$