Results 1 to 3 of 3

Thread: Homogenous D.E. with Non-Constant Coefficients

  1. October 12th 2011, 03:40 PM #1
    jegues
    jegues is offline
    Member
    Joined
    Jan 2010
    Posts
    144

    Question Homogenous D.E. with Non-Constant Coefficients

    How do I go about solving this differential equation?

    I can't remember if we even covered this in my calculus class, but as soon as I see the solution it should jog my memory.

    0 = 4\frac{dy}{dx} + x\frac{d^{2}y}{(dx)^{2}} \quad \text{where} \quad y=f(x)

    Thanks again!
    Follow Math Help Forum on Facebook and Google+
  2. October 12th 2011, 03:45 PM #2
    Danny
    Danny is offline
    MHF Contributor Danny's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,311
    Thanks
    4

    Re: Homogenous D.E. with Non-Constant Coefficients

    Since your ODE has no y, if you let \dfrac{dy}{dx} = u then \dfrac{d^2y}{dx^2} = \dfrac{d u}{d x} and substitute, your ODE will separate.
    Follow Math Help Forum on Facebook and Google+
  3. October 12th 2011, 08:42 PM #3
    Prove It
    Prove It is offline
    MHF Contributor Prove It's Avatar
    Joined
    Aug 2008
    Posts
    10,266
    Thanks
    701

    Re: Homogenous D.E. with Non-Constant Coefficients

    Quote Originally Posted by Danny View Post
    Since your ODE has no y, if you let \dfrac{dy}{dx} = u then \dfrac{d^2y}{dx^2} = \dfrac{d u}{d x} and substitute, your ODE will separate.
    And is also first-order linear...
    Follow Math Help Forum on Facebook and Google+
« Find curve that has tangent and normal lines that create a triangle | Laplace Transform of a 2nd order Differential Equation »

Similar Math Help Forum Discussions

  1. Second order ODE with non-constant coefficients
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: October 21st 2011, 07:39 PM
  2. 2nd order DE's with constant coefficients.
    Posted in the Differential Equations Forum
    Replies: 6
    Last Post: January 9th 2011, 07:19 AM
  3. Need Help with second order DE with constant coefficients.
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: December 17th 2010, 07:25 AM
  4. Second order linear homogenous Differential Equation with constant coefficients
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: March 31st 2010, 12:24 AM
  5. ODE - constant coefficients
    Posted in the Calculus Forum
    Replies: 9
    Last Post: December 28th 2008, 07:46 AM

Search Tags


/mathhelpforum @mathhelpforum