Results 1 to 5 of 5

Math Help - Second-order linear homogeneous diff. eq. with constant coefficients

  1. #1
    Newbie
    Joined
    Mar 2011
    Posts
    8

    Second-order linear homogeneous diff. eq. with constant coefficients

    I have the following diff.eq. (d^2)y/d(x^2) + 2 dy/dx + y = 0 , but I don't have the answer, so could you please check.

    The general solution that I got is y= e^(-x)[Ax+B]
    If we have that x=0 when y=3 and dy/dx=1 , Then the particular solution is y= e^(-x)[4x+3]?

    And another one, which is inhomogenous:

    (d^2)y/d(x^2) + 2 dy/dx + y = x+2
    General solution: y= e^(-x)[Ax+B] + x^2-4x+8
    when x=0, y=3 and dy/dx=1
    Particular solution: y= e^(-x)[10x-5] + x^2-4x+8

    Sry but I don't have the nerves to type-write the full solutions,however I took pictures: ImageShack Album - 8 images

    Does someone know a good online calculator for second order diff. eq ? I tried wolfram alpha but it seems that it doesn't solve these type of eqs.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by Tron View Post
    I have the following diff.eq. (d^2)y/d(x^2) + 2 dy/dx + y = 0 , but I don't have the answer, so could you please check.

    The general solution that I got is y= e^(-x)[Ax+B]
    If we have that x=0 when y=3 and dy/dx=1 , Then the particular solution is y= e^(-x)[4x+3]?

    And another one, which is inhomogenous:

    (d^2)y/d(x^2) + 2 dy/dx + y = x+2
    General solution: y= e^(-x)[Ax+B] + x^2-4x+8
    when x=0, y=3 and dy/dx=1
    Particular solution: y= e^(-x)[10x-5] + x^2-4x+8

    Sry but I don't have the nerves to type-write the full solutions,however I took pictures: ImageShack Album - 8 images

    Does someone know a good online calculator for second order diff. eq ? I tried wolfram alpha but it seems that it doesn't solve these type of eqs.
    Here is what wolfram alpha gives

    dsolve y''(x)+2y'(x)+ y(x)=x+2 - Wolfram|Alpha

    You will need to solve for the arbitrary constants!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,962
    Thanks
    349
    Awards
    1
    Quote Originally Posted by Tron View Post
    I have the following diff.eq. (d^2)y/d(x^2) + 2 dy/dx + y = 0 , but I don't have the answer, so could you please check.

    The general solution that I got is y= e^(-x)[Ax+B]
    If we have that x=0 when y=3 and dy/dx=1 , Then the particular solution is y= e^(-x)[4x+3]?

    And another one, which is inhomogenous:

    (d^2)y/d(x^2) + 2 dy/dx + y = x+2
    General solution: y= e^(-x)[Ax+B] + x^2-4x+8
    when x=0, y=3 and dy/dx=1
    Particular solution: y= e^(-x)[10x-5] + x^2-4x+8

    Sry but I don't have the nerves to type-write the full solutions,however I took pictures: ImageShack Album - 8 images

    Does someone know a good online calculator for second order diff. eq ? I tried wolfram alpha but it seems that it doesn't solve these type of eqs.
    Surely you can put your solutions through the differential equation to check them?

    Your answer to the homogeneous equation is correct, but the particular solution for the inhomogeneous equation is wrong. Try plugging your particular solution back into the inhomogeneous equation again. Or note that the particular solution will be of the form ax + b, not a quadratic.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Mar 2011
    Posts
    8
    Quote Originally Posted by topsquark View Post
    Surely you can put your solutions through the differential equation to check them?

    Your answer to the homogeneous equation is correct, but the particular solution for the inhomogeneous equation is wrong. Try plugging your particular solution back into the inhomogeneous equation again. Or note that the particular solution will be of the form ax + b, not a quadratic.

    -Dan
    Hi

    I checked with wolfram that my general solution to the inhomogenous is correct.
    Whatever the values of A and B are for the particular solution, they won't change the second part of the equation ( the P.I.) , so it must stay x^2-4x+8 ?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,962
    Thanks
    349
    Awards
    1
    Quote Originally Posted by Tron View Post
    Hi

    I checked with wolfram that my general solution to the inhomogenous is correct.
    Whatever the values of A and B are for the particular solution, they won't change the second part of the equation ( the P.I.) , so it must stay x^2-4x+8 ?
    Please read the post I made before:
    Quote Originally Posted by topsquark View Post
    Surely you can put your solutions through the differential equation to check them?

    Your answer to the homogeneous equation is correct, but the particular solution for the inhomogeneous equation is wrong. Try plugging your particular solution back into the inhomogeneous equation again. Or note that the particular solution will be of the form ax + b, not a quadratic.

    -Dan
    Your particular solution is incorrect. Use the form yp = ax + b, then recalculate A and B.

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: May 3rd 2011, 11:39 AM
  2. Replies: 1
    Last Post: January 22nd 2011, 02:04 PM
  3. Non-homogeneous 2nd order DE with constant coefficients.
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: April 8th 2010, 12:15 PM
  4. Second-Order Linear Non Homogeneous ODE with Constant Coefficients
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: October 22nd 2009, 11:13 PM
  5. Replies: 1
    Last Post: July 29th 2007, 02:37 PM

Search Tags


/mathhelpforum @mathhelpforum