Results 1 to 5 of 5

Thread: Need a general solution checked

  1. #1
    Senior Member
    Joined
    Apr 2010
    Posts
    487

    Need a general solution checked

    The question:
    Write down the form of the particular solution you should try when solving the non-homogeneous differential equation
    \frac{d^2y}{dx^2} - 8\frac{dy}{dx} + 16y = 2e^{4x}

    My answer:

    y_p = Cx^2e^{4x}

    Does this look correct? Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    10
    Quote Originally Posted by Glitch View Post
    The question:
    Write down the form of the particular solution you should try when solving the non-homogeneous differential equation
    \frac{d^2y}{dx^2} - 8\frac{dy}{dx} + 16y = 2e^{4x}

    My answer:

    y_p = Cx^2e^{4x}

    Does this look correct? Thanks.
    y''-8y'+16y=0

    (m-4)^2=0

    y_p=C_1e^{4x}+C_2xe^{4x}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    12,861
    Thanks
    1941
    Quote Originally Posted by dwsmith View Post
    y''-8y'+16y=0

    (m-4)^2=0

    y_p=C_1e^{4x}+C_2xe^{4x}
    What you've written is the Characteristic Solution, not the Particular Solution.

    Since your RHS of the DE is of the family \displaystyle e^{4x}, you would normally choose \displaystyle Ce^{4x} as a particular solution.

    But since \displaystyle e^{4x} appears in your Characteristic Solution, you would then normally choose \displaystyle Cx\,e^{4x} as a particular solution.

    But since \displaystyle x\,e^{4x} appears in your Characteristic Solution, you would then normally choose \displaystyle Cx^2e^{4x} as a particular solution.

    So I agree with the OP's choice of \displaystyle y_p = Cx^2e^{4x}.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    10
    Quote Originally Posted by Prove It View Post
    What you've written is the Characteristic Solution, not the Particular Solution.

    Since your RHS of the DE is of the family \displaystyle e^{4x}, you would normally choose \displaystyle Ce^{4x} as a particular solution.

    But since \displaystyle e^{4x} appears in your Characteristic Solution, you would then normally choose \displaystyle Cx\,e^{4x} as a particular solution.

    But since \displaystyle x\,e^{4x} appears in your Characteristic Solution, you would then normally choose \displaystyle Cx^2e^{4x} as a particular solution.

    So I agree with the OP's choice of \displaystyle y_p = Cx^2e^{4x}.
    I have selective reading. I only read homogeneous and not non-homogeneous.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Apr 2010
    Posts
    487
    Sorry, my title was probably misleading. Thanks guys.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: Nov 21st 2010, 05:10 PM
  2. General Solution of a differential solution
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: Sep 11th 2010, 03:49 AM
  3. general solution
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: Oct 8th 2009, 08:50 AM
  4. Finding the general solution from a given particular solution.
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: Oct 7th 2009, 02:44 AM
  5. find the general solution when 1 solution is given
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: Mar 4th 2009, 10:09 PM

Search Tags


/mathhelpforum @mathhelpforum