Answer
$y=x-2x^2+3$
Work Step by Step
$$y-x\frac{dy}{dx}=3-2x^2\frac{dy}{dx}$$
$$y-3=x\frac{dy}{dx}-2x^2\frac{dy}{dx}$$
$$y-3=(x-2x^2)\frac{dy}{dx}$$
$$(y-3)dx=(x-2x^2)dy$$
Multiply the entire equation by $\frac{1}{(y-3)(x-2x^2)}$ to separate variables.
$$\frac{1}{(y-3)(x-2x^2)}[(y-3)dx=(x-2x^2)dy]$$
$$\frac{dx}{x-2x^2}=\frac{dy}{y-3}$$
Since each side of the equation is in terms of a variable, you can integrate.
$$\int \frac{dx}{x-2x^2}=\int \frac{dy}{y-3}$$
$$\ln|x-2x^2|=\ln|y-3|$$
Solve for $y$.
$$x-2x^2=y-3$$
$$y=x-2x^2+3$$
