Final answer:
To solve the given differential equation y' + 2xy² = 0 using the separable method, separate the variables by dividing both sides by y². Integrate both sides with respect to y and solve for y.
Step-by-step explanation:
To solve the given differential equation using the separable method, we need to separate the variables. The given equation is y' + 2xy² = 0. Rearranging the equation, we have y' = -2xy². Now we can separate the variables by dividing both sides by y², which gives y' / y² = -2x. Integrating both sides with respect to y, we get ∫y' / y² dy = ∫-2x dx. The left side of the equation becomes -1/y = -x² + C, where C is the constant of integration. Solving for y, we have y = -1 / (-x² + C).