Solve y=ydy

$$y = y d y$$

Solve for d

$$\left\{\begin{matrix}d=\frac{1}{y}\text{, }&y\neq 0\\d\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply y and y to get y^{2}.

$$y=y^{2}d$$

Swap sides so that all variable terms are on the left hand side.

$$y^{2}d=y$$

Divide both sides by y^{2}.

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

Dividing by y^{2} undoes the multiplication by y^{2}.

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

Divide y by y^{2}.

$$d=\frac{1}{y}$$

Solve for y

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y=\frac{1}{d}\text{, }&d\neq 0\end{matrix}\right.$$