Solve ydx+(x^2-4x)dy=0

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

Solve for d (complex solution)

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&x=3\text{ or }x=0\text{ or }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x^{2}-4x by d.

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

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

$$ydx+x^{2}dy-4xdy=0$$

Combine ydx and -4xdy to get -3ydx.

$$-3ydx+x^{2}dy=0$$

Combine all terms containing d.

$$\left(-3yx+x^{2}y\right)d=0$$

The equation is in standard form.

$$\left(yx^{2}-3xy\right)d=0$$

Divide 0 by -3yx+x^{2}y.

$$d=0$$

Solve for d

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&x=3\text{ or }x=0\text{ or }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x^{2}-4x by d.

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

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

$$ydx+x^{2}dy-4xdy=0$$

Combine ydx and -4xdy to get -3ydx.

$$-3ydx+x^{2}dy=0$$

Combine all terms containing d.

$$\left(-3yx+x^{2}y\right)d=0$$

The equation is in standard form.

$$\left(yx^{2}-3xy\right)d=0$$

Divide 0 by -3yx+x^{2}y.

$$d=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=3\text{; }x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&d=0\text{ or }y=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}\\x=3\text{; }x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&d=0\text{ or }y=0\end{matrix}\right.$$