Differential equation given integrating factor

  1. 1. The problem statement, all variables and given/known data

    Show that given function μ is an integrating factor and solve the differential equation..

    y^2 dx + (1 + xy) dy = 0 ; μ(x) = e^xy

    3. The attempt at a solution

    let M = y^2
    N = (1 + xy)

    dM/dy = 2y dN/dx = y hence, not exact equation.

    times μ(x) = e^xy to the not exact equations...

    2y(e^xy) dx + y(e^xy) dy = 0

    let M = 2y(e^xy)
    N = y(e^xy)

    dM/dy = 2(e^xy) + 2y(e^y) ---> apply product rule

    dN/dx = 0(e^xy) + y(e^y) ---> apply product rule

    the problem is.. the equations still not the exact equations..
    How to proceed?
  2. jcsd
  3. HallsofIvy

    HallsofIvy 41,265
    Staff Emeritus
    Science Advisor

    Yes- which means that [itex]\mu= e^{xy}[/itex] is NOT an integrating factor. Something is wrong with that question.
  4. So... i can't solve this equation? the equation doesn't have any solutions?
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