Results 1 to 2 of 2

Math Help - Find the general solution of the following Cauchy-Euler differential equations.

  1. #1
    Member
    Joined
    Nov 2008
    Posts
    75

    Find the general solution of the following Cauchy-Euler differential equations.

    2x^3(y''')-3x^2(y'')+5xy'=0
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5
    Let's suppose to search as solution of the DE...

    2x^{3}\cdot y^{'''} - 2x^{2}\cdot y^{''} + 5x\cdot y^{'}=0 (1)

    ... function of the type y=x^{\alpha}. Is...

    y^{'} = \alpha\cdot x^{\alpha-1}

    y^{''} = \alpha\cdot (\alpha-1)\cdot x^{\alpha-2}

    y^{'''} = \alpha\cdot (\alpha-1)\cdot (\alpha-2)\cdot x^{\alpha-3} (2)

    ... and the substitution of (2) in (1) leads us to write...

    2\cdot \alpha\cdot (\alpha-1)\cdot (\alpha-2) - 3\cdot \alpha\cdot (\alpha-1) + 5\cdot \alpha =0 (3)

    If \alpha_{1}, \alpha_{1} and \alpha_{3} are the roots ot the algebraic third order equation (3), then the general solution of (1) will be...

    y= c_{1}\cdot x^{\alpha_{1}} + c_{2}\cdot x^{\alpha_{2}} + c_{3}\cdot x^{\alpha_{3}} (4)

    Kind regards

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. general solution of differential equations
    Posted in the Differential Equations Forum
    Replies: 10
    Last Post: April 6th 2011, 03:17 AM
  2. [SOLVED] Differential Equations General solution help.
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: November 5th 2010, 05:19 PM
  3. Differential Equations General Solution
    Posted in the Differential Equations Forum
    Replies: 9
    Last Post: May 22nd 2009, 06:30 AM
  4. general solution for differential equations
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: December 10th 2008, 02:19 PM
  5. Numerical solution of differential equations (Euler method)
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: October 27th 2008, 04:12 PM

Search Tags


/mathhelpforum @mathhelpforum