Results 1 to 2 of 2

Math Help - [SOLVED] Differential Equation General Solution Help

  1. #1
    Newbie
    Joined
    May 2008
    Posts
    10

    [SOLVED] Differential Equation General Solution Help

    hey guys, i'm really struggling with this and need someone to point me in the right direction, any help at all would be greatly appreciated!

    Find the general solution of Eq.2 and hence the general solution for y(x). Your answer should have 2 arbitrary constants of integration.

    Here are the equation's i've got so far:

    1. \frac{dy}{dx}=\frac{{\rho}g}{T}\int^x_{0}\sqrt{1+\  frac{dy}{dt}^2}dt

    Differentiating both sides of Eq.1 to produce second order ODE for y(x)

    \frac{d^2y}{dx^2}=\frac{{\rho}g}{T}\sqrt{1+\frac{d  y}{dx}^2}

    By letting u=\frac{dy}{dx}

    2.
    \frac{du}{dx}=\frac{{\rho}g}{T}\sqrt{1+u^2}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Dec 2007
    From
    Anchorage, AK
    Posts
    276
    Note that your resulting equation is separable:
    \frac{du}{dx}=\frac{{\rho}g}{T}\sqrt{1+u^2}
    \frac{du}{\sqrt{1+u^2}}=\frac{{\rho}g}{T}\,dx
    Integrate both sides and solve for u(x), remembering your constant of integration. Then, use u(x)=y'(x), and integrate to find y(x) (with your second constant of integration).

    --Kevin C.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. general solution of this differential equation?
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: September 10th 2010, 08:57 AM
  2. general solution of a differential equation
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: December 5th 2009, 08:30 AM
  3. General Solution to Differential Equation
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: June 1st 2009, 01:12 PM
  4. General Solution of Differential Equation
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: December 7th 2008, 04:13 PM
  5. General Solution to a Differential Equation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 9th 2007, 03:48 PM

Search Tags


/mathhelpforum @mathhelpforum