Solve frac{a_{y}}{d_{x}}-x^2=x^2*y

$$\frac { a _ { y } } { d _ { x } } - x ^ { 2 } = x ^ { 2 } \cdot y$$

Solve for d_x

$$\left\{\begin{matrix}d_{x}=\frac{a_{y}}{\left(y+1\right)x^{2}}\text{, }&a_{y}\neq 0\text{ and }y\neq -1\text{ and }x\neq 0\\d_{x}\neq 0\text{, }&\left(x=0\text{ or }y=-1\right)\text{ and }a_{y}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable d_{x} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by d_{x}.

$$a_{y}-x^{2}d_{x}=x^{2}yd_{x}$$

Subtract x^{2}yd_{x} from both sides.

$$a_{y}-x^{2}d_{x}-x^{2}yd_{x}=0$$

Subtract a_{y} from both sides. Anything subtracted from zero gives its negation.

$$-x^{2}d_{x}-x^{2}yd_{x}=-a_{y}$$

Combine all terms containing d_{x}.

$$\left(-x^{2}-x^{2}y\right)d_{x}=-a_{y}$$

The equation is in standard form.

$$\left(-x^{2}-yx^{2}\right)d_{x}=-a_{y}$$

Divide both sides by -x^{2}-x^{2}y.

$$\frac{\left(-x^{2}-yx^{2}\right)d_{x}}{-x^{2}-yx^{2}}=-\frac{a_{y}}{-x^{2}-yx^{2}}$$

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

$$d_{x}=-\frac{a_{y}}{-x^{2}-yx^{2}}$$

Divide -a_{y} by -x^{2}-x^{2}y.

$$d_{x}=\frac{a_{y}}{\left(y+1\right)x^{2}}$$

Variable d_{x} cannot be equal to 0.

$$d_{x}=\frac{a_{y}}{\left(y+1\right)x^{2}}\text{, }d_{x}\neq 0$$

Solve for a_y

$$a_{y}=d_{x}\left(y+1\right)x^{2}$$

$$d_{x}\neq 0$$