Solve dy/dy=y+x/2xy

$$\frac { d y } { d y } = \frac { y + x } { 2 x y }$$

Solve for x

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

$$y\neq 0\text{ and }y\neq \frac{1}{2}$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2xy.

$$2xy\frac{\mathrm{d}}{\mathrm{d}y}(y)=y+x$$

Subtract x from both sides.

$$2xy\frac{\mathrm{d}}{\mathrm{d}y}(y)-x=y$$

Combine all terms containing x.

$$\left(2y\frac{\mathrm{d}}{\mathrm{d}y}(y)-1\right)x=y$$

The equation is in standard form.

$$\left(2y-1\right)x=y$$

Divide both sides by 2y-1.

$$\frac{\left(2y-1\right)x}{2y-1}=\frac{y}{2y-1}$$

Dividing by 2y-1 undoes the multiplication by 2y-1.

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

Variable x cannot be equal to 0.

$$x=\frac{y}{2y-1}\text{, }x\neq 0$$

Solve for y

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

$$x\neq 0\text{ and }x\neq \frac{1}{2}$$