Results 1 to 2 of 2

Thread: Finding a DE from a 2nd Order General Solution

  1. #1
    MHF Contributor Jason76's Avatar
    Joined
    Oct 2012
    From
    USA
    Posts
    1,314
    Thanks
    21

    Finding a DE from a 2nd Order General Solution

    In order to find a DE from the general solution of a first order equation, we use implicit differention, so should we try implicit differentition twice to find the DE from solution to a 2nd order equation?

    How about

    $\displaystyle y = c_{1}e^{-2x} + c_{2}e^{3x}$ ?

    Now if we had a general solution to a first order one like

    $\displaystyle y = x^{2} + C$

    then

    $\displaystyle 1(y') = 2x + 0$

    $\displaystyle y' = 2x$

    or

    $\displaystyle \dfrac{dy}{dx} = 2x$

    or

    $\displaystyle dy = 2x dx$ would be the DE.
    Last edited by Jason76; Aug 1st 2015 at 02:03 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member GLaw's Avatar
    Joined
    Jul 2015
    From
    Ilford
    Posts
    217
    Thanks
    113
    Quote Originally Posted by Jason76 View Post
    so should we try implicit differentition twice to find the DE from solution to a 2nd order equation?
    Yes indeed. The idea is to have an equation that does not involve any of the arbitrary constants in the general solution.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: Jul 25th 2015, 08:06 AM
  2. Replies: 1
    Last Post: Oct 30th 2010, 04:30 PM
  3. General Solution 2nd order
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: May 5th 2010, 03:26 PM
  4. the general solution to a first order ODE
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: Mar 12th 2010, 07:08 AM
  5. 2nd order PDE- general solution
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: Nov 9th 2009, 08:02 AM

Search Tags


/mathhelpforum @mathhelpforum