Solve dv/dt=-kv^2/m

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

Solve for k

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

Steps for Solving Linear Equation

Multiply both sides of the equation by m.

$$m\frac{\mathrm{d}}{\mathrm{d}t}(v)=-kv^{2}$$

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

$$-kv^{2}=m\frac{\mathrm{d}}{\mathrm{d}t}(v)$$

The equation is in standard form.

$$\left(-v^{2}\right)k=0$$

Divide 0 by -v^{2}.

$$k=0$$

Solve for m

$$m\neq 0$$

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

Steps for Solving Linear Equation

Variable m cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by m.

$$m\frac{\mathrm{d}}{\mathrm{d}t}(v)=-kv^{2}$$

The equation is in standard form.

$$0=-kv^{2}$$

This is false for any m.

$$m\in$$