Solve tany=dx/xdy

$$\tan y = \frac { d x } { x d y }$$

Solve for d

$$d\neq 0$$

$$x\neq 0\text{ and }\tan(y)-\frac{1}{y}=0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }y=\frac{\pi \left(2n_{1}+1\right)}{2}\text{ and }y\neq 0$$

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 dxy.

$$dxy\tan(y)=dx$$

Subtract dx from both sides.

$$dxy\tan(y)-dx=0$$

Combine all terms containing d.

$$\left(xy\tan(y)-x\right)d=0$$

Divide 0 by xy\tan(y)-x.

$$d=0$$

Variable d cannot be equal to 0.

$$d\in \emptyset$$

Solve for x

$$x\neq 0$$

$$d\neq 0\text{ and }\tan(y)-\frac{1}{y}=0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }y=\frac{\pi \left(2n_{1}+1\right)}{2}\text{ and }y\neq 0$$

Steps for Solving Linear Equation

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

$$dxy\tan(y)=dx$$

Subtract dx from both sides.

$$dxy\tan(y)-dx=0$$

Combine all terms containing x.

$$\left(dy\tan(y)-d\right)x=0$$

Divide 0 by dy\tan(y)-d.

$$x=0$$

Variable x cannot be equal to 0.

$$x\in \emptyset$$