d y = x d x
Solve for d (complex solution)
\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&y=x^{2}\end{matrix}\right.
Solve for d
\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&y=x^{2}\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}\\x=-\sqrt{y}\text{; }x=\sqrt{y}\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&d=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\sqrt{y}\text{; }x=-\sqrt{y}\text{, }&y\geq 0\\x\in \mathrm{R}\text{, }&d=0\end{matrix}\right.
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dy=x^{2}d
Multiply x and x to get x^{2}.
dy-x^{2}d=0
Subtract x^{2}d from both sides.
-dx^{2}+dy=0
Reorder the terms.
\left(-x^{2}+y\right)d=0
Combine all terms containing d.
\left(y-x^{2}\right)d=0
The equation is in standard form.
d=0
Divide 0 by y-x^{2}.
dy=x^{2}d
Multiply x and x to get x^{2}.
dy-x^{2}d=0
Subtract x^{2}d from both sides.
-dx^{2}+dy=0
Reorder the terms.
\left(-x^{2}+y\right)d=0
Combine all terms containing d.
\left(y-x^{2}\right)d=0
The equation is in standard form.
d=0
Divide 0 by y-x^{2}.
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