Bernoulli Differential Equations

[courtrigrad]

Solve the equation \frac{dy}{dx}-y = -xe^{-2x}y^{3}.

So a Bernoulli differential equation is in the form \frac{dy}{dx} + P(x)y = Q(x)y^{n}. Isn't the above equation in this form already?I set u = y^{-2} and \frac{du}{dx} = -2y^{-3.

So -2y^{-3} + 2y^{-2} = 2xe^{-2x}. From here what do I do?

Is the integrating factor I(x) = e^{\int -1 dx} = e^{-x}?

Thanks

 

[courtrigrad]

nvm got it.