Solve dv/mg*kv^2=dt/m

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

Solve for d (complex solution)

$$\left\{\begin{matrix}d=0\text{, }&m\neq 0\text{ and }g\neq 0\text{ and }k\neq 0\text{ and }v\neq 0\\d\in \mathrm{C}\text{, }&v=\frac{1}{gkt}\text{ and }g\neq 0\text{ and }k\neq 0\text{ and }m\neq 0\text{ and }t\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by gkmv^{2}, the least common multiple of mgkv^{2},m.

$$dv=gkv^{2}dt$$

Subtract gkv^{2}dt from both sides.

$$dv-gkv^{2}dt=0$$

Reorder the terms.

$$-dgktv^{2}+dv=0$$

Combine all terms containing d.

$$\left(-gktv^{2}+v\right)d=0$$

The equation is in standard form.

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

Divide 0 by -gktv^{2}+v.

$$d=0$$

Solve for d

$$\left\{\begin{matrix}d=0\text{, }&m\neq 0\text{ and }g\neq 0\text{ and }k\neq 0\text{ and }v\neq 0\\d\in \mathrm{R}\text{, }&v=\frac{1}{gkt}\text{ and }g\neq 0\text{ and }t\neq 0\text{ and }k\neq 0\text{ and }m\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by gkmv^{2}, the least common multiple of mgkv^{2},m.

$$dv=gkv^{2}dt$$

Subtract gkv^{2}dt from both sides.

$$dv-gkv^{2}dt=0$$

Reorder the terms.

$$-dgktv^{2}+dv=0$$

Combine all terms containing d.

$$\left(-gktv^{2}+v\right)d=0$$

The equation is in standard form.

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

Divide 0 by -gktv^{2}+v.

$$d=0$$

Solve for g

$$\left\{\begin{matrix}g=\frac{1}{ktv}\text{, }&t\neq 0\text{ and }k\neq 0\text{ and }v\neq 0\text{ and }m\neq 0\\g\neq 0\text{, }&d=0\text{ and }k\neq 0\text{ and }v\neq 0\text{ and }m\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable g cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by gkmv^{2}, the least common multiple of mgkv^{2},m.

$$dv=gkv^{2}dt$$

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

$$gkv^{2}dt=dv$$

The equation is in standard form.

$$dktv^{2}g=dv$$

Divide both sides by kv^{2}dt.

$$\frac{dktv^{2}g}{dktv^{2}}=\frac{dv}{dktv^{2}}$$

Dividing by kv^{2}dt undoes the multiplication by kv^{2}dt.

$$g=\frac{dv}{dktv^{2}}$$

Divide dv by kv^{2}dt.

$$g=\frac{1}{ktv}$$

Variable g cannot be equal to 0.

$$g=\frac{1}{ktv}\text{, }g\neq 0$$