Solve dL/L=tdt

$$\frac { d L } { L } = t d t$$

Solve for L

$$L\neq 0$$

$$d=0\text{ or }|t|=1$$

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.

$$dL=tdtL$$

Multiply t and t to get t^{2}.

$$dL=t^{2}dL$$

Subtract t^{2}dL from both sides.

$$dL-t^{2}dL=0$$

Reorder the terms.

$$-Ldt^{2}+Ld=0$$

Combine all terms containing L.

$$\left(-dt^{2}+d\right)L=0$$

The equation is in standard form.

$$\left(d-dt^{2}\right)L=0$$

Divide 0 by d-dt^{2}.

$$L=0$$

Variable L cannot be equal to 0.

$$L\in \emptyset$$

Solve for d

$$\left\{\begin{matrix}d=0\text{, }&L\neq 0\\d\in \mathrm{R}\text{, }&L\neq 0\text{ and }|t|=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by L.

$$dL=tdtL$$

Multiply t and t to get t^{2}.

$$dL=t^{2}dL$$

Subtract t^{2}dL from both sides.

$$dL-t^{2}dL=0$$

Reorder the terms.

$$-Ldt^{2}+Ld=0$$

Combine all terms containing d.

$$\left(-Lt^{2}+L\right)d=0$$

The equation is in standard form.

$$\left(L-Lt^{2}\right)d=0$$

Divide 0 by -Lt^{2}+L.

$$d=0$$