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

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

Solve for d

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

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

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$y\frac{\mathrm{d}(x)}{\mathrm{d}y}+2dx+y\times 3=0$$

Subtract y\frac{\mathrm{d}(x)}{\mathrm{d}y} from both sides. Anything subtracted from zero gives its negation.

$$2dx+y\times 3=-y\frac{\mathrm{d}(x)}{\mathrm{d}y}$$

Subtract y\times 3 from both sides.

$$2dx=-y\frac{\mathrm{d}(x)}{\mathrm{d}y}-y\times 3$$

Multiply -1 and 3 to get -3.

$$2dx=-y\frac{\mathrm{d}(x)}{\mathrm{d}y}-3y$$

The equation is in standard form.

$$2xd=-3y$$

Divide both sides by 2x.

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

Dividing by 2x undoes the multiplication by 2x.

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

Solve for x

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

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