Solve 1/2ydy=dx

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

Solve for d (complex solution)

$$\left\{\begin{matrix}d=0\text{, }&y\neq 0\\d\in \mathrm{C}\text{, }&x=\frac{1}{2}\text{ and }y\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2y.

$$1dy=dx\times 2y$$

Subtract dx\times 2y from both sides.

$$1dy-dx\times 2y=0$$

Reorder the terms.

$$dy-2dxy=0$$

Combine all terms containing d.

$$\left(y-2xy\right)d=0$$

Divide 0 by y-2xy.

$$d=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{1}{2}\text{, }&y\neq 0\\x\in \mathrm{C}\text{, }&d=0\text{ and }y\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2y.

$$1dy=dx\times 2y$$

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

$$dx\times 2y=1dy$$

Reorder the terms.

$$2dxy=dy$$

The equation is in standard form.

$$2dyx=dy$$

Divide both sides by 2dy.

$$\frac{2dyx}{2dy}=\frac{dy}{2dy}$$

Dividing by 2dy undoes the multiplication by 2dy.

$$x=\frac{dy}{2dy}$$

Divide dy by 2dy.

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

Solve for d

$$\left\{\begin{matrix}d=0\text{, }&y\neq 0\\d\in \mathrm{R}\text{, }&x=\frac{1}{2}\text{ and }y\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2y.

$$1dy=dx\times 2y$$

Subtract dx\times 2y from both sides.

$$1dy-dx\times 2y=0$$

Reorder the terms.

$$dy-2dxy=0$$

Combine all terms containing d.

$$\left(y-2xy\right)d=0$$

Divide 0 by y-2xy.

$$d=0$$

Solve for x

$$\left\{\begin{matrix}x=\frac{1}{2}\text{, }&y\neq 0\\x\in \mathrm{R}\text{, }&d=0\text{ and }y\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2y.

$$1dy=dx\times 2y$$

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

$$dx\times 2y=1dy$$

Reorder the terms.

$$2dxy=dy$$

The equation is in standard form.

$$2dyx=dy$$

Divide both sides by 2dy.

$$\frac{2dyx}{2dy}=\frac{dy}{2dy}$$

Dividing by 2dy undoes the multiplication by 2dy.

$$x=\frac{dy}{2dy}$$

Divide dy by 2dy.

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