Solve y=4x^2y/dx

$$y = 4 x ^ { 2 } \frac { y } { d x }$$

Solve for d

$$\left\{\begin{matrix}d=4x\text{, }&x\neq 0\\d\neq 0\text{, }&y=0\text{ and }x\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable d cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by dx.

$$ydx=4x^{2}y$$

Reorder the terms.

$$dxy=4yx^{2}$$

The equation is in standard form.

$$xyd=4yx^{2}$$

Divide both sides by xy.

$$\frac{xyd}{xy}=\frac{4yx^{2}}{xy}$$

Dividing by xy undoes the multiplication by xy.

$$d=\frac{4yx^{2}}{xy}$$

Divide 4yx^{2} by xy.

$$d=4x$$

Variable d cannot be equal to 0.

$$d=4x\text{, }d\neq 0$$

Solve for x

$$\left\{\begin{matrix}x=\frac{d}{4}\text{, }&d\neq 0\\x\neq 0\text{, }&y=0\text{ and }d\neq 0\end{matrix}\right.$$