Thread: Help with non linear differential equation

I have come across this question:

dy/dx - y = xy^5

How do you solve this?

It's Bernoulli.

Originally Posted by Ackbeet

It's Bernoulli.

Oh yeh, thanks. I'll have an attempt now

Right. Let me know if you have difficulty.

Originally Posted by Ackbeet

Right. Let me know if you have difficulty.

Quick question:

If z = y^-4 , how do you get y on it's own?

y = z^4 ?
Or y = z^-1/4 ?

The second method is correct. Or you can do implicit differentiation to translate the DE to z's. One possibly useful equation is y^4 = 1/z.