Results 1 to 2 of 2

Math Help - Differential equation solution

  1. #1
    Junior Member
    Joined
    Nov 2009
    From
    Australia
    Posts
    56

    Differential equation solution

    Hello,
    I don't understand what the following question is asking - may I ask for someone to elaborate?:

    "By considering the differential of z(x)=f(x)y(x), find the solution of the following differential equation:"

    (x^2+4)dy/dx + 2xy =0 where y(1) =5

    I've looked up solving differential equations, but most involve integration, which we have not touched on in lectures yet.
    Or am I completely off track?

    Thank you in advance for any feedback
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,315
    Thanks
    1224
    The left hand side is a product rule expansion of \frac{d}{dx}[(x^2 + 4)y].


    So \frac{d}{dx}[(x^2 + 4)y] = 0

    (x^2 + 4)y = \int{0\,dx}

    (x^2 + 4)y = C

    y = \frac{C}{x^2 + 4}.


    Now using the boundary condition

    5 = \frac{C}{1^2 + 4}

    5 = \frac{C}{5}

    25 = C.


    Therefore the solution is

    y = \frac{25}{x^2 + 4}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Verify Solution of Differential equation
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: August 29th 2011, 08:49 PM
  2. differential equation solution
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: September 29th 2010, 03:04 AM
  3. Is this a solution to the differential equation?
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: May 21st 2010, 06:19 PM
  4. Particular Solution to Differential Equation!!!
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: May 29th 2009, 12:14 PM
  5. solution of a differential equation
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: November 7th 2008, 07:18 PM

Search Tags


/mathhelpforum @mathhelpforum