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Math Help - 2 ODE questions

  1. #1
    Newbie
    Joined
    May 2010
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    2 ODE questions

    How do I show, that (x, 1+x) is a fundamental set for the equation
    (1-x)*(dy/dx)+2x*(dy/dx)-2y=0
    and state an open interval where I belongs to R on which y=cx+d(1+x) is the unique solution to the equation (c and d being arbitrary constants)

    and

    how do I find the general solution to
    (d^4y/dx^4)+8(dy/dx)-9y=e^x-sin(x)

    Thanks for your time
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  2. #2
    Newbie
    Joined
    Jul 2010
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    London
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    For your second problem, just treat it as you would a 2nd order ODE
    ie solve the homogeonous eqn y''''+8y''-9y=0 by trying y=me^x.
    This gives you a quartic auxilliary eqn to solve which in turn gives you the complementary function.

    then find the particular integral by trying the solution y=Exe^x+Fsinx+Gcosx to find E,F,G.

    add the complementary function to the particular integral to get the general solution.

    Can't help with your first problem, sorry...
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  3. #3
    A Plied Mathematician
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    For your first problem, just show that x and 1+x are both solutions to the DE, and then use the Wronskian to show linear independence.
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