Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to integrate this partial differential equation

  1. Dec 28, 2012 #1
    I have the following equation

    [itex]\frac{\partial}{\partial y}\left(m\frac{dy}{dx}\right)=0[/itex]

    where [itex]y[/itex] is a function of [itex]x[/itex] and [itex]m[/itex] is a function of [itex]y[/itex]. If I integrate this equation first with respect to [itex]y[/itex] should I get a function of [itex]x[/itex] as the constant of integration (say [itex]C\left(x\right)[/itex]) or it is just a constant? If it is a function, how can I then find its form (e.g. polynomial, etc.)? Should I use boundary conditions or I can decide about the form from inspecting the type of the equation.
  2. jcsd
  3. Dec 28, 2012 #2
    Yes, you should have
    And therefore you can solve it by
    Which you can integrate.
  4. Dec 28, 2012 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You'll have to use boundary conditions. There's nothing in the equation that gives a clue about the form of C(x).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook