Bernoulli Differential Equation?

[jofree87]

I keep getting stuck on one part of the equation. can somebody help?

dy/dx = y(xy³ - 1)

dy/dx = xy⁴ - y

dy/dx + y = xy⁴

u = y^1-n = y^-3

y = u^-3

dy/dx = dy/du * du/dx

dy/dx = -3u^-4 du/dx

Substituting terms into the original equation

-3u^-4 du/dx + u^-3 = x(u^-3)⁴

Here is where I get stuck. When I divide u^-4 to clean up the equation, the right hand side still has u^-8 remaining. I will not be able to go on since the right hand side can only have x terms. What am I doing wrong?

 

[tiny-tim]

Hi jofree87!

u = y^1-n = y^-3

y = u^-3

erm … noooo!