Solve dy=x^3dx

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

Solve for d (complex solution)

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&y=x^{4}\end{matrix}\right.$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$dy=x^{4}d$$

Subtract x^{4}d from both sides.

$$dy-x^{4}d=0$$

Reorder the terms.

$$-dx^{4}+dy=0$$

Combine all terms containing d.

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

The equation is in standard form.

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

Divide 0 by y-x^{4}.

$$d=0$$

Solve for d

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&y=x^{4}\end{matrix}\right.$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$dy=x^{4}d$$

Subtract x^{4}d from both sides.

$$dy-x^{4}d=0$$

Reorder the terms.

$$-dx^{4}+dy=0$$

Combine all terms containing d.

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

The equation is in standard form.

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

Divide 0 by y-x^{4}.

$$d=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=i\sqrt[4]{y}\text{; }x=\sqrt[4]{y}\text{; }x=-\sqrt[4]{y}\text{; }x=-i\sqrt[4]{y}\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&d=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\sqrt[4]{y}\text{; }x=-\sqrt[4]{y}\text{, }&y\geq 0\\x\in \mathrm{R}\text{, }&d=0\end{matrix}\right.$$