Solve 2ydy=4xdx

$$2 y d y = 4 x d x$$

Solve for d (complex solution)

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&y=-\sqrt{2}x\text{ or }y=\sqrt{2}x\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply y and y to get y^{2}.

$$2y^{2}d=4xdx$$

Multiply x and x to get x^{2}.

$$2y^{2}d=4x^{2}d$$

Subtract 4x^{2}d from both sides.

$$2y^{2}d-4x^{2}d=0$$

Combine all terms containing d.

$$\left(2y^{2}-4x^{2}\right)d=0$$

Divide 0 by 2y^{2}-4x^{2}.

$$d=0$$

Solve for d

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&|y|=\sqrt{2}|x|\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply y and y to get y^{2}.

$$2y^{2}d=4xdx$$

Multiply x and x to get x^{2}.

$$2y^{2}d=4x^{2}d$$

Subtract 4x^{2}d from both sides.

$$2y^{2}d-4x^{2}d=0$$

Combine all terms containing d.

$$\left(2y^{2}-4x^{2}\right)d=0$$

Divide 0 by 2y^{2}-4x^{2}.

$$d=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=-\frac{\sqrt{2}y}{2}\text{; }x=\frac{\sqrt{2}y}{2}\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&d=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}\\x=\frac{\sqrt{2}y}{2}\text{; }x=-\frac{\sqrt{2}y}{2}\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&d=0\end{matrix}\right.$$