Solve x/dy=sqrt{y}

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

Solve for d (complex solution)

$$d=y^{-\frac{3}{2}}x$$

$$y\neq 0\text{ and }x\neq 0$$

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 dy.

$$x=dy\sqrt{y}$$

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

$$dy\sqrt{y}=x$$

The equation is in standard form.

$$\sqrt{y}yd=x$$

Divide both sides by y\sqrt{y}.

$$\frac{\sqrt{y}yd}{\sqrt{y}y}=\frac{x}{\sqrt{y}y}$$

Dividing by y\sqrt{y} undoes the multiplication by y\sqrt{y}.

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

Divide x by y\sqrt{y}.

$$d=y^{-\frac{3}{2}}x$$

Variable d cannot be equal to 0.

$$d=y^{-\frac{3}{2}}x\text{, }d\neq 0$$

Solve for x (complex solution)

$$x=dy^{\frac{3}{2}}$$

$$d\neq 0\text{ and }y\neq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\frac{1}{dy}x=\sqrt{y}$$

Divide both sides by d^{-1}y^{-1}.

$$\frac{\frac{1}{dy}xdy}{1}=\frac{\sqrt{y}dy}{1}$$

Dividing by d^{-1}y^{-1} undoes the multiplication by d^{-1}y^{-1}.

$$x=\frac{\sqrt{y}dy}{1}$$

Divide \sqrt{y} by d^{-1}y^{-1}.

$$x=dy^{\frac{3}{2}}$$

Solve for d

$$d=\frac{x}{y^{\frac{3}{2}}}$$

$$x\neq 0\text{ and }y>0$$

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 dy.

$$x=dy\sqrt{y}$$

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

$$dy\sqrt{y}=x$$

The equation is in standard form.

$$\sqrt{y}yd=x$$

Divide both sides by y\sqrt{y}.

$$\frac{\sqrt{y}yd}{\sqrt{y}y}=\frac{x}{\sqrt{y}y}$$

Dividing by y\sqrt{y} undoes the multiplication by y\sqrt{y}.

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

Divide x by y\sqrt{y}.

$$d=\frac{x}{y^{\frac{3}{2}}}$$

Variable d cannot be equal to 0.

$$d=\frac{x}{y^{\frac{3}{2}}}\text{, }d\neq 0$$

Solve for x

$$x=dy^{\frac{3}{2}}$$

$$d\neq 0\text{ and }y>0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\frac{1}{dy}x=\sqrt{y}$$

Divide both sides by d^{-1}y^{-1}.

$$\frac{\frac{1}{dy}xdy}{1}=\frac{\sqrt{y}dy}{1}$$

Dividing by d^{-1}y^{-1} undoes the multiplication by d^{-1}y^{-1}.

$$x=\frac{\sqrt{y}dy}{1}$$

Divide \sqrt{y} by d^{-1}y^{-1}.

$$x=dy^{\frac{3}{2}}$$