Solve dx/x=e^2xdx

$$\frac { d x } { x } = e ^ { 2 x } d x$$

Solve for d

$$\left\{\begin{matrix}d=0\text{, }&x\neq 0\\d\in \mathrm{R}\text{, }&1-xe^{2x}=0\text{ and }x\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$dx=e^{2x}dxx$$

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

$$dx=e^{2x}dx^{2}$$

Subtract e^{2x}dx^{2} from both sides.

$$dx-e^{2x}dx^{2}=0$$

Reorder the terms.

$$-dx^{2}e^{2x}+dx=0$$

Combine all terms containing d.

$$\left(-x^{2}e^{2x}+x\right)d=0$$

The equation is in standard form.

$$\left(x-x^{2}e^{2x}\right)d=0$$

Divide 0 by -x^{2}e^{2x}+x.

$$d=0$$