Solve dv/dt+k/mv^2=1/m

$$\frac { d v } { d t } + \frac { k } { m v ^ { 2 } } = 1 / m$$

Solve for m

$$m\neq 0$$

$$k=v^{2}\text{ and }v\neq 0$$

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 mv^{2}, the least common multiple of mv^{2},m.

$$mv^{2}\frac{\mathrm{d}}{\mathrm{d}t}(v)+k=v^{2}$$

Subtract k from both sides.

$$mv^{2}\frac{\mathrm{d}}{\mathrm{d}t}(v)=v^{2}-k$$

The equation is in standard form.

$$0=v^{2}-k$$

This is false for any m.

$$m\in$$

Solve for k

$$k=v^{2}$$

$$m\neq 0\text{ and }v\neq 0$$