Solve e^-2xdx=d(2-e^-2x)

$$e ^ { - 2 x } d x = d ( 2 - e ^ { - 2 x } )$$

Solve for d (complex solution)

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&\frac{x-2e^{2x}+1}{e^{2x}}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract d\left(2-e^{-2x}\right) from both sides.

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

Use the distributive property to multiply -d by 2-e^{-2x}.

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

Combine all terms containing d.

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

The equation is in standard form.

$$\left(\frac{x}{e^{2x}}+\frac{1}{e^{2x}}-2\right)d=0$$

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

$$d=0$$

Solve for d

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&\frac{x-2e^{2x}+1}{e^{2x}}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract d\left(2-e^{-2x}\right) from both sides.

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

Use the distributive property to multiply -d by 2-e^{-2x}.

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

Combine all terms containing d.

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

The equation is in standard form.

$$\left(\frac{x}{e^{2x}}+\frac{1}{e^{2x}}-2\right)d=0$$

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

$$d=0$$