Solve dy=sqrt[5]{x^2}

$$d y = \sqrt[ 5 ] { x ^ { 2 } }$$

Solve for d (complex solution)

$$\left\{\begin{matrix}d=\frac{x^{\frac{2}{5}}}{y}\text{, }&y\neq 0\\d\in \mathrm{C}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$yd=\sqrt[5]{x^{2}}$$

Divide both sides by y.

$$\frac{yd}{y}=\frac{x^{\frac{2}{5}}}{y}$$

Dividing by y undoes the multiplication by y.

$$d=\frac{x^{\frac{2}{5}}}{y}$$

Solve for d

$$\left\{\begin{matrix}d=\frac{x^{\frac{2}{5}}}{y}\text{, }&y\neq 0\\d\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$yd=\sqrt[5]{x^{2}}$$

Divide both sides by y.

$$\frac{yd}{y}=\frac{x^{\frac{2}{5}}}{y}$$

Dividing by y undoes the multiplication by y.

$$d=\frac{x^{\frac{2}{5}}}{y}$$

Solve for x (complex solution)

$$x=-d^{\frac{5}{2}}y^{\frac{5}{2}}$$

$$x=d^{\frac{5}{2}}y^{\frac{5}{2}}\text{, }arg(dy)<\frac{2\pi }{5}\text{ or }y=0\text{ or }d=0$$

Solve for x

$$x=\left(dy\right)^{\frac{5}{2}}$$

$$x=-\left(dy\right)^{\frac{5}{2}}\text{, }\left(y\geq 0\text{ and }d\geq 0\right)\text{ or }\left(d\leq 0\text{ and }y\leq 0\right)$$