Solve 5xy-5x^3-8arctan(x/e)=3pi

$$5xy-5 { x }^{ 3 } -8 \arctan ( \frac{ x }{ e } ) = 3 \pi$$

Solve for y

$$y=\frac{8\arctan(\frac{x}{e})+5x^{3}+3\pi }{5x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Add 8\arctan(\frac{x}{e}) to both sides.

$$5xy-5x^{3}=3\pi +8\arctan(\frac{x}{e})$$

Add 5x^{3} to both sides.

$$5xy=3\pi +8\arctan(\frac{x}{e})+5x^{3}$$

The equation is in standard form.

$$5xy=8\arctan(\frac{x}{e})+5x^{3}+3\pi$$

Divide both sides by 5x.

$$\frac{5xy}{5x}=\frac{8\arctan(\frac{x}{e})+5x^{3}+3\pi }{5x}$$

Dividing by 5x undoes the multiplication by 5x.

$$y=\frac{8\arctan(\frac{x}{e})+5x^{3}+3\pi }{5x}$$

Divide 3\pi +8\arctan(\frac{x}{e})+5x^{3} by 5x.

$$y=\frac{\frac{8\arctan(\frac{x}{e})+3\pi }{x}+5x^{2}}{5}$$