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Math Help - Challenging Differential Equation (For you, it''s probably cake)

  1. #1
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    Challenging Differential Equation (For you, it''s probably cake)

    http://www.math.rutgers.edu/~songyun...examreview.pdf

    Does anyone know how to do problem 10 here?

    I got the rest, but this one is confusing and I don't know what to do.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    You're homogeneous solution is x = Ae^(-t)cos(t) +Be^(-t)*sin(t)

    How did you go about trying to find the particular solution?

    If you use undetermined coefficients

    xp = Cte^(-t)cos(t) +Dte^(-t)*sin(t) you have to multiply by t since

    e^(-t)*sin(t) and e^(-t)*cos(t) are homogeneous solutions

    If you use variation of parameters W = e^(-2*t)

    you obtain z1' = -sin(t)^2 z2 ' = sin(t)cos(t)
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