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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Bernoulli Differential Equations

**Physics Forums | Science Articles, Homework Help, Discussion**