Solve aby/dx=y

$$a \frac { b y } { d x } = y$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Multiply both sides of the equation by dx.

$$aby=ydx$$

Reorder the terms.

$$aby=dxy$$

The equation is in standard form.

$$bya=dxy$$

Divide both sides by by.

$$\frac{bya}{by}=\frac{dxy}{by}$$

Dividing by by undoes the multiplication by by.

$$a=\frac{dxy}{by}$$

Divide dxy by by.

$$a=\frac{dx}{b}$$

Solve for b (complex solution)

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

Steps for Solving Linear Equation

Multiply both sides of the equation by dx.

$$aby=ydx$$

Reorder the terms.

$$aby=dxy$$

The equation is in standard form.

$$ayb=dxy$$

Divide both sides by ay.

$$\frac{ayb}{ay}=\frac{dxy}{ay}$$

Dividing by ay undoes the multiplication by ay.

$$b=\frac{dxy}{ay}$$

Divide dxy by ay.

$$b=\frac{dx}{a}$$

Solve for a

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

Steps for Solving Linear Equation

Multiply both sides of the equation by dx.

$$aby=ydx$$

Reorder the terms.

$$aby=dxy$$

The equation is in standard form.

$$bya=dxy$$

Divide both sides by by.

$$\frac{bya}{by}=\frac{dxy}{by}$$

Dividing by by undoes the multiplication by by.

$$a=\frac{dxy}{by}$$

Divide dxy by by.

$$a=\frac{dx}{b}$$

Solve for b

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

Steps for Solving Linear Equation

Multiply both sides of the equation by dx.

$$aby=ydx$$

Reorder the terms.

$$aby=dxy$$

The equation is in standard form.

$$ayb=dxy$$

Divide both sides by ay.

$$\frac{ayb}{ay}=\frac{dxy}{ay}$$

Dividing by ay undoes the multiplication by ay.

$$b=\frac{dxy}{ay}$$

Divide dxy by ay.

$$b=\frac{dx}{a}$$