Solve dx^2=ydy

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

Solve for d (complex solution)

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

Steps for Solving Linear Equation

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

$$dx^{2}=y^{2}d$$

Subtract y^{2}d from both sides.

$$dx^{2}-y^{2}d=0$$

Reorder the terms.

$$dx^{2}-dy^{2}=0$$

Combine all terms containing d.

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

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

$$d=0$$

Solve for d

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

Steps for Solving Linear Equation

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

$$dx^{2}=y^{2}d$$

Subtract y^{2}d from both sides.

$$dx^{2}-y^{2}d=0$$

Reorder the terms.

$$dx^{2}-dy^{2}=0$$

Combine all terms containing d.

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

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

$$d=0$$

Solve for x (complex solution)

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

Solve for x

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