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Differential Equations help!

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    ReputationRep:
    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!
  2. Online

    ReputationRep:
    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)

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