Solving Bernoulli ODE | Step-by-Step Guide | Example with n=-2

[cue928]

I am working on the following Bernoulli ODE: 3xy^2 y' = 3x^4 + y^3. I come up with n = -2, so v = y^3 and y' = (1/3)v^(-2/3) v'. My integrating factor was x^-1. I end up with y^3 = X^2 + Cx yet the book has the same thing except X^4 instead of X^2. That makes me think I'm going wrong with multiplying it through but I don't see where.

 

[tiny-tim]

hi cue928!

(try using the X² icon just above the Reply box )

My integrating factor was x^-1. I end up with y^3 = X^2 + Cx yet the book has the same thing except X^4 instead of X^2.

it should have worked …

show us how you got the x²​

 

[cue928]

It was right, I just made a stupid mistake that led me to think it was something bigger than what it really was.