Solve 2dy/dx+y^2-3=0

$$\frac { 2 d y } { d x } + y ^ { 2 } - 3 = 0$$

Solve for d (complex solution)

$$d\neq 0$$

$$x=-\frac{2y}{y^{2}-3}\text{ and }y\neq -\sqrt{3}\text{ and }y\neq \sqrt{3}\text{ and }y\neq 0$$

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 dx.

$$2dy+dxy^{2}+dx\left(-3\right)=0$$

Reorder the terms.

$$dxy^{2}-3dx+2dy=0$$

Combine all terms containing d.

$$\left(xy^{2}-3x+2y\right)d=0$$

Divide 0 by 2y-3x+xy^{2}.

$$d=0$$

Variable d cannot be equal to 0.

$$d\in \emptyset$$

Solve for x (complex solution)

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

$$y\neq 0\text{ and }y\neq -\sqrt{3}\text{ and }y\neq \sqrt{3}\text{ and }d\neq 0$$

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 dx.

$$2dy+dxy^{2}+dx\left(-3\right)=0$$

Subtract 2dy from both sides. Anything subtracted from zero gives its negation.

$$dxy^{2}+dx\left(-3\right)=-2dy$$

Combine all terms containing x.

$$\left(dy^{2}+d\left(-3\right)\right)x=-2dy$$

The equation is in standard form.

$$\left(dy^{2}-3d\right)x=-2dy$$

Divide both sides by dy^{2}-3d.

$$\frac{\left(dy^{2}-3d\right)x}{dy^{2}-3d}=-\frac{2dy}{dy^{2}-3d}$$

Dividing by dy^{2}-3d undoes the multiplication by dy^{2}-3d.

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

Divide -2dy by dy^{2}-3d.

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

Variable x cannot be equal to 0.

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

Solve for d

$$d\neq 0$$

$$x=-\frac{2y}{y^{2}-3}\text{ and }|y|\neq \sqrt{3}\text{ and }y\neq 0$$

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 dx.

$$2dy+dxy^{2}+dx\left(-3\right)=0$$

Reorder the terms.

$$dxy^{2}-3dx+2dy=0$$

Combine all terms containing d.

$$\left(xy^{2}-3x+2y\right)d=0$$

Divide 0 by 2y-3x+xy^{2}.

$$d=0$$

Variable d cannot be equal to 0.

$$d\in \emptyset$$

Solve for x

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

$$y\neq 0\text{ and }|y|\neq \sqrt{3}\text{ and }d\neq 0$$

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 dx.

$$2dy+dxy^{2}+dx\left(-3\right)=0$$

Subtract 2dy from both sides. Anything subtracted from zero gives its negation.

$$dxy^{2}+dx\left(-3\right)=-2dy$$

Combine all terms containing x.

$$\left(dy^{2}+d\left(-3\right)\right)x=-2dy$$

The equation is in standard form.

$$\left(dy^{2}-3d\right)x=-2dy$$

Divide both sides by dy^{2}-3d.

$$\frac{\left(dy^{2}-3d\right)x}{dy^{2}-3d}=-\frac{2dy}{dy^{2}-3d}$$

Dividing by dy^{2}-3d undoes the multiplication by dy^{2}-3d.

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

Divide -2dy by dy^{2}-3d.

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

Variable x cannot be equal to 0.

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