Solve 1/Lv_{L}dt=di

$$\frac { 1 } { L } v _ { L } d t = d i$$

Solve for L

$$\left\{\begin{matrix}L=-itv_{L}\text{, }&t\neq 0\text{ and }v_{L}\neq 0\\L\neq 0\text{, }&d=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$1v_{L}dt=diL$$

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

$$diL=1v_{L}dt$$

Reorder the terms.

$$iLd=dtv_{L}$$

The equation is in standard form.

$$idL=dtv_{L}$$

Divide both sides by id.

$$\frac{idL}{id}=\frac{dtv_{L}}{id}$$

Dividing by id undoes the multiplication by id.

$$L=\frac{dtv_{L}}{id}$$

Divide v_{L}dt by id.

$$L=-itv_{L}$$

Variable L cannot be equal to 0.

$$L=-itv_{L}\text{, }L\neq 0$$

Solve for d

$$\left\{\begin{matrix}d=0\text{, }&L\neq 0\\d\in \mathrm{C}\text{, }&t=\frac{iL}{v_{L}}\text{ and }v_{L}\neq 0\text{ and }L\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by L.

$$1v_{L}dt=diL$$

Subtract diL from both sides.

$$1v_{L}dt-diL=0$$

Reorder the terms.

$$dtv_{L}-iLd=0$$

Combine all terms containing d.

$$\left(tv_{L}-iL\right)d=0$$

Divide 0 by -iL+v_{L}t.

$$d=0$$