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Math Help - 4th order ode: private solution

  1. #1
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    Question 4th order ode: private solution

    Dear all
    Hi,

    I seek the solution of the 4th order ordinary differential equation as follows:

    d^4(y) / dx^4 + G * y = H

    for the homogenous relation which is:
    d^4(y) / dx^4 + G * y = 0
    or
    G=4*b^4
    d^4(y) / dx^4 + 4*b^4 * y = 0

    we assume the solution of the bellow form:
    y=exp(b*x)*(A*cos(b*x)+B*sin(b*x))+exp(-b*x)*(C*cos(b*x)+D*sin(b*x))
    4th order ode: private solution-eq1.jpg

    Now what is the private solution for the inhomogenous equation?
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  2. #2
    Grand Panjandrum
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    Nov 2005
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    Re: 4th order ode: private solution

    Quote Originally Posted by nsvcivil View Post
    Dear all
    Hi,

    I seek the solution of the 4th order ordinary differential equation as follows:

    d^4(y) / dx^4 + G * y = H

    for the homogenous relation which is:
    d^4(y) / dx^4 + G * y = 0
    or
    G=4*b^4
    d^4(y) / dx^4 + 4*b^4 * y = 0

    we assume the solution of the bellow form:
    y=exp(b*x)*(A*cos(b*x)+B*sin(b*x))+exp(-b*x)*(C*cos(b*x)+D*sin(b*x))
    Click image for larger version. 

Name:	eq1.JPG 
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ID:	23222

    Now what is the private solution for the inhomogenous equation?
    Assuming H is a constant, a particular integral is the constant function y(x)=H/(4b^4)

    CB
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