[HuyTaa]

Can someone give me a step by step guide of how to intergrate this?
x(dy/dx) = 2y + 1/y
Thanks! and any useful techniques of doing similar ones!

[Hasufel]

you can start by collecting terms on the RHS, so the equation looks like:

x(dy/dx) = (2y^2+1)/y,

then take the reciprocal of each side, to get:

(1/x)(dx/dy) = y/(2y^2+1)

multiply both sides by dy:

(1/x)dx =[ y/(2y^2+1)]dy

what do you notice about the RHS? - could it be like: f '(x)/ f(x) ? - you`ll need to give f ' (x) a factor of 4, while multiplying the RHS by (1/4)

EDIT: the key point about this technique - called "seperation of variables" - is exactly that - that you are able to physically "seperate" the x`s from the y`s on either side of (or sometimes the same side) the equation (don`t forget to add the constant to the x side)