Solve x/dx+2xy=2x

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

Solve for d

$$d=-\frac{1}{2x\left(y-1\right)}$$

$$y\neq 1\text{ and }x\neq 0$$

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 dx.

$$x+2xydx=2xdx$$

Multiply x and x to get x^{2}.

$$x+2x^{2}yd=2xdx$$

Multiply x and x to get x^{2}.

$$x+2x^{2}yd=2x^{2}d$$

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

$$x+2x^{2}yd-2x^{2}d=0$$

Subtract x from both sides. Anything subtracted from zero gives its negation.

$$2x^{2}yd-2x^{2}d=-x$$

Combine all terms containing d.

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

The equation is in standard form.

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

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

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

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

$$d=-\frac{x}{2yx^{2}-2x^{2}}$$

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

$$d=-\frac{1}{2x\left(y-1\right)}$$

Variable d cannot be equal to 0.

$$d=-\frac{1}{2x\left(y-1\right)}\text{, }d\neq 0$$

Solve for x

$$x=-\frac{1}{2d\left(y-1\right)}$$

$$y\neq 1\text{ and }d\neq 0$$