Solve (x^24+y^14)dx-xy^13dy=0

$$( x ^ { 2 } 4 + y ^ { 14 } ) d x - x y ^ { 13 } d y = 0$$

Solve for d (complex solution)

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

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 13 and 1 to get 14.

$$\left(x^{2}\times 4+y^{14}\right)dx-xy^{14}d=0$$

Use the distributive property to multiply x^{2}\times 4+y^{14} by d.

$$\left(4x^{2}d+y^{14}d\right)x-xy^{14}d=0$$

Use the distributive property to multiply 4x^{2}d+y^{14}d by x.

$$4dx^{3}+y^{14}dx-xy^{14}d=0$$

Combine y^{14}dx and -xy^{14}d to get 0.

$$4dx^{3}=0$$

The equation is in standard form.

$$4x^{3}d=0$$

Divide 0 by 4x^{3}.

$$d=0$$

Solve for d

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

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 13 and 1 to get 14.

$$\left(x^{2}\times 4+y^{14}\right)dx-xy^{14}d=0$$

Use the distributive property to multiply x^{2}\times 4+y^{14} by d.

$$\left(4x^{2}d+y^{14}d\right)x-xy^{14}d=0$$

Use the distributive property to multiply 4x^{2}d+y^{14}d by x.

$$4dx^{3}+y^{14}dx-xy^{14}d=0$$

Combine y^{14}dx and -xy^{14}d to get 0.

$$4dx^{3}=0$$

The equation is in standard form.

$$4x^{3}d=0$$

Divide 0 by 4x^{3}.

$$d=0$$

Solve for x (complex solution)

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

Solve for x

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