Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By Jester

Math Help - help solving this differential equation

  1. #1
    Member
    Joined
    Mar 2009
    Posts
    182
    Thanks
    1

    help solving this differential equation

    Hi all, i'm trying to solve the following DE which I have attached as an image, as well as written it in the title box as my Latex sucks.

    2sinh(x)y'' - 2cosh(x)y' + ysinh^3(x) = 0

    help solving this differential equation-ode.png

    If someone can explain the method used to solve this, that would be really helpful

    Thanks
    Last edited by mash; March 6th 2014 at 10:06 AM. Reason: fixed latex
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,392
    Thanks
    56

    Re: 2sinh(x)y'' - 2cosh(x)y' + ysinh^3(x) = 0

    Here's what I might try

    First $\dfrac{d}{dx} \left(\dfrac{y'}{\sinh x}\right) = \dfrac{\sinh x \,y '' - \cosh x \,y'}{\sinh ^2 x}$

    So your DE becomes

    $2 \dfrac{d}{dx} \left(\dfrac{y'}{\sinh x}\right) +\sinh x \,y = 0$

    or

    $2 \dfrac{1}{\sinh x } \,\dfrac{d}{dx} \left(\dfrac{y'}{\sinh x}\right) +y = 0$

    Now try a new substitution. Let $ t = \cosh x$.

    See how that goes.
    Thanks from mash
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum