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First order linear diff eq

  1. May 15, 2012 #1
    1. The problem statement, all variables and given/known data

    Screenshot2012-05-15at41120AM.png



    I don't understand why in step 2 dy turns into d and why +P(x) dissappears
    I also don't see a difference between v(x)y and v(x)*y

    In step three why does the d disappear. I see that dx is going over to the right side, well, what about the numerator d?
     
  2. jcsd
  3. May 15, 2012 #2
    d/dx is the differential operator. dy/dx just means d/dx operating on y. You should probably read a bit more elementary calculus to get used to this notation.

    You start from a differential equation
    [tex] \frac{dy}{dx} + P(x) y = Q(x) [/tex]
    and then you multiply both sides of this equation with a function [itex]v(x) [/itex] (which you have to find first) which has the property that the left hand sides of steps 1 and 2 are equal.

    In step 3, you integrate both sides of the equation with respect to x.
     
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