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Math Help - Plotting a second order differential equation

  1. #1
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    Plotting a second order differential equation

    Hi,

    I'm trying to plot d^2y/dx^2=-y.

    I think that the way forward is to solve the equation to get one in terms of x and y (but maybe there is a better way?). This gives me the auxiliary quadratic
    (m^2) -1=0, so m=ħi

    So the complimentary function is of the form y=Acosx+Bsinx.

    But now I am stuck... I don't know how to find the particular integral. I used the trial solution y=λxsinx but didn't get anywhere.

    Thanks
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  2. #2
    A Plied Mathematician
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    Typically, for plotting solutions for a DE, you need initial or boundary conditions in order to eliminate the arbitrary constants that, since you're always integrating to solve a DE, always show up. If you have initial conditions, then plug those in and get yourself a system of two equations in two unknowns in order to solve for A and B. Make sense?
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