Results 1 to 5 of 5

Math Help - 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
    5
    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
    11,408
    Thanks
    1294
    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
    5
    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: November 21st 2010, 04:10 PM
  2. General Solution of a differential solution
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: September 11th 2010, 02:49 AM
  3. general solution
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: October 8th 2009, 07:50 AM
  4. Finding the general solution from a given particular solution.
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: October 7th 2009, 01:44 AM
  5. find the general solution when 1 solution is given
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: March 4th 2009, 09:09 PM

Search Tags


/mathhelpforum @mathhelpforum