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Im stuck

  1. May 18, 2004 #1
    ok
    im trying to solve the following equation using standard aux method:

    d^2y/dx^2 + 3dy/dy +2y = cos x with conditions x(0)=-3 and x'(0) = 3

    my aux eqn is:

    ae^x + be^-2x

    and my yp is;

    a sin kx + b cos kx

    i differentiate this twice and substitute into the original equation, and i get:

    (-a sin x - b cos x)+3(a cos x-b sin x) + 2(a sin x+ b cos x) = cos x.

    Now at this stage im not sure if this is right or not, can someone please confirm if this is right or not.

    I ve done this question using the laplace method and the answer i get is;

    -19/2e^x +32/5 e^2x + 1/10 cos x - 3/10 sin x.

    Here my aux equation is not the same as what i get when i apply the laplace method.

    Im not sure what is going wrong.
    Someone help me please.
     
  2. jcsd
  3. May 18, 2004 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    you have a and b representing two different numbers simlutaneously.

    if you're not sure which of e^2x or e^-2x is correct why don't you subs it into the equation to see which one works? i think it is -2, i also think you want e^-x and not e^x since the aux equation is m^2+3m+2=(m+1)(m+2)
     
  4. May 18, 2004 #3
    solution

    Hi;
    Here is your solution:
    [tex]
    y(x)=\frac{3sinx}{10}+\frac{cosx}{10}-\frac{7e^{-x}}{2}+\frac{2e^{-2x}}{5}
    [/tex]
    Best of luck,
    Max.
    P.S. Obtained by Maxima: http://maxima.sourceforge.net/download.shtml
     
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