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.