Solve dQ/Q=tdt

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

Solve for Q

$$Q\neq 0$$

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

Steps for Solving Linear Equation

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

$$dQ=tdtQ$$

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

$$dQ=t^{2}dQ$$

Subtract t^{2}dQ from both sides.

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

Reorder the terms.

$$-Qdt^{2}+Qd=0$$

Combine all terms containing Q.

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

The equation is in standard form.

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

Divide 0 by d-dt^{2}.

$$Q=0$$

Variable Q cannot be equal to 0.

$$Q\in \emptyset$$

Solve for d

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

Steps for Solving Linear Equation

Multiply both sides of the equation by Q.

$$dQ=tdtQ$$

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

$$dQ=t^{2}dQ$$

Subtract t^{2}dQ from both sides.

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

Reorder the terms.

$$-Qdt^{2}+Qd=0$$

Combine all terms containing d.

$$\left(-Qt^{2}+Q\right)d=0$$

The equation is in standard form.

$$\left(Q-Qt^{2}\right)d=0$$

Divide 0 by -Qt^{2}+Q.

$$d=0$$