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Math Help - differential equation help for old time learner please !!!

  1. #1
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    differential equation help for old time learner please !!!

    hi i have been out of education for quite a while now and im trying to get back into the swing of maths and such since im starting a engineering degree in september and havent been doing much maths since my national certificate years ago now .. im strugling with findind the particular solutions for differential equation. could some one please talk me through this question and the stages i would take to come to the final answer thankyou Bill .

    4 d^2 y/ dx^2 + 12 dy/dx +9y = 0 given y=2 and dy/dx=1 at x=0


    much apriciated if some maths wiz could help me out thanks
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  2. #2
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    Quote Originally Posted by oldboy26 View Post
    hi i have been out of education for quite a while now and im trying to get back into the swing of maths and such since im starting a engineering degree in september and havent been doing much maths since my national certificate years ago now .. im strugling with findind the particular solutions for differential equation. could some one please talk me through this question and the stages i would take to come to the final answer thankyou Bill .

    4 d^2 y/ dx^2 + 12 dy/dx +9y = 0 given y=2 and dy/dx=1 at x=0


    much apriciated if some maths wiz could help me out thanks
    Google the following:

    Second order differential equation constant coefficients

    and find a website that works for you.
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  3. #3
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    This is a second order linear homogeneous constant coefficient DE.

    The characteristic equation is \displaystyle 4m^2 + 12m + 9 = 0

    The solution of the DE is \displaystyle y = C_1e^{m_1 x} + C_2e^{m_2 x}, where \displaystyle m_1, m_2 are the solutions to the characteristic equation.
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