Solve -kx=md^2x/dt^2

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

Solve for k

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

Steps for Solving Linear Equation

Reorder the terms.

$$-kx=m\frac{\mathrm{d}(x)}{\mathrm{d}t^{2}}$$

The equation is in standard form.

$$\left(-x\right)k=0$$

Divide 0 by -x.

$$k=0$$

Solve for m

$$m\in \mathrm{R}$$

$$x=0\text{ or }k=0$$

Steps for Solving Linear Equation

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

$$m\frac{\mathrm{d}(x)}{\mathrm{d}t^{2}}=\left(-k\right)x$$

Reorder the terms.

$$m\frac{\mathrm{d}(x)}{\mathrm{d}t^{2}}=-kx$$

The equation is in standard form.

$$0=-kx$$

This is false for any m.

$$m\in$$