Solve the equation [tex] \frac{dy}{dx}-y = -xe^{-2x}y^{3} [/tex].(adsbygoogle = window.adsbygoogle || []).push({});

So a Bernoulli differential equation is in the form [tex] \frac{dy}{dx} + P(x)y = Q(x)y^{n} [/tex]. Isn't the above equation in this form already?

I set [tex] u = y^{-2} [/tex] and [tex] \frac{du}{dx} = -2y^{-3 [/tex].

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

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

Thanks

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# Bernoulli Differential Equations

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