Solve e^x-e^-x=2y

$$e ^ { x } - e ^ { - x } = 2 y$$

Solve for y

$$y=\frac{e^{x}}{2}-\frac{1}{2e^{x}}$$

Steps for Solving Linear Equation

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

$$2y=e^{x}-e^{-x}$$

The equation is in standard form.

$$2y=-\frac{1}{e^{x}}+e^{x}$$

Divide both sides by 2.

$$\frac{2y}{2}=\frac{-\frac{1}{e^{x}}+e^{x}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$y=\frac{-\frac{1}{e^{x}}+e^{x}}{2}$$

Divide e^{x}-\frac{1}{e^{x}} by 2.

$$y=\frac{e^{x}}{2}-\frac{1}{2e^{x}}$$

Solve for x

$$x=\ln(\sqrt{y^{2}+1}+y)$$