Solve y=x^2dx

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

Solve for d (complex solution)

$$\left\{\begin{matrix}d=\frac{y}{x^{3}}\text{, }&x\neq 0\\d\in \mathrm{C}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$y=x^{3}d$$

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

$$x^{3}d=y$$

Divide both sides by x^{3}.

$$\frac{x^{3}d}{x^{3}}=\frac{y}{x^{3}}$$

Dividing by x^{3} undoes the multiplication by x^{3}.

$$d=\frac{y}{x^{3}}$$

Solve for d

$$\left\{\begin{matrix}d=\frac{y}{x^{3}}\text{, }&x\neq 0\\d\in \mathrm{R}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$y=x^{3}d$$

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

$$x^{3}d=y$$

Divide both sides by x^{3}.

$$\frac{x^{3}d}{x^{3}}=\frac{y}{x^{3}}$$

Dividing by x^{3} undoes the multiplication by x^{3}.

$$d=\frac{y}{x^{3}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=e^{\frac{2\pi i}{3}}d^{-\frac{1}{3}}\sqrt[3]{y}\text{; }x=d^{-\frac{1}{3}}\sqrt[3]{y}\text{; }x=e^{\frac{4\pi i}{3}}d^{-\frac{1}{3}}\sqrt[3]{y}\text{, }&d\neq 0\\x\in \mathrm{C}\text{, }&y=0\text{ and }d=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\sqrt[3]{\frac{y}{d}}\text{, }&d\neq 0\\x\in \mathrm{R}\text{, }&y=0\text{ and }d=0\end{matrix}\right.$$