Solve 3y=1/sqrt{1-2x^2}-e^2x-1

$$3y = \frac{ 1 }{ \sqrt{ 1-2 { x }^{ 2 } } } - { e }^{ 2x-1 }$$

Solve for y (complex solution)

$$y=\frac{-e^{2x-1}+\left(1-2x^{2}\right)^{-\frac{1}{2}}}{3}$$

$$x\neq -\frac{\sqrt{2}}{2}\text{ and }x\neq \frac{\sqrt{2}}{2}$$

Steps for Solving Linear Equation

The equation is in standard form.

$$3y=-e^{2x-1}+\frac{1}{\sqrt{1-2x^{2}}}$$

Divide both sides by 3.

$$\frac{3y}{3}=\frac{-e^{2x-1}+\left(1-2x^{2}\right)^{-\frac{1}{2}}}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$y=\frac{-e^{2x-1}+\left(1-2x^{2}\right)^{-\frac{1}{2}}}{3}$$

Solve for y

$$y=-\frac{e^{2x-1}}{3}+\frac{1}{3\sqrt{1-2x^{2}}}$$

$$|x|<\frac{\sqrt{2}}{2}$$

Steps for Solving Linear Equation

The equation is in standard form.

$$3y=-e^{2x-1}+\frac{1}{\sqrt{1-2x^{2}}}$$

Divide both sides by 3.

$$\frac{3y}{3}=\frac{-e^{2x-1}+\frac{1}{\sqrt{1-2x^{2}}}}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$y=\frac{-e^{2x-1}+\frac{1}{\sqrt{1-2x^{2}}}}{3}$$

Divide -e^{2x-1}+\frac{1}{\sqrt{1-2x^{2}}} by 3.

$$y=-\frac{e^{2x-1}}{3}+\frac{1}{3\sqrt{1-2x^{2}}}$$