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Math Help - [SOLVED] Second order differential equations

  1. #1
    Junior Member
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    [SOLVED] Second order differential equations

    a)
    Find the general solution of the second order differential equation
    4
    y′′ + 8y+ 3y = 0 .

    Find the particular solution that satisfies the initial conditions y(0) = 2 and y(0) = 1/2.

    I got the general solution to be:

    y(x) = (c^(A))e^((-3/2)x)+(c^(B))e^((-1/2)x)

    and by intitial condiotion I got the particular solution to be:

    y(x) = (-3/2)e^((-3/2)x)+(7/2)e^((-1/2)x)

    Are my answers right... help would be appreciated thank you
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  2. #2
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    hELLO, rajr!

    Find the general solution of the second order differential equation: . 4y''+ 8y' + 3y \:=\: 0

    Find the particular solution that satisfies the initial conditions: . y(0) = 2 and y'(0) = 1


    I got the general solution to be: . y(x) \:= C_1e^{-\frac{3}{2}x}+ C_2e^{-\frac{1}{2}x}

    and by intitial conditions, I got the particular solution to be: . y(x) \:= \:-\tfrac{3}{2}e^{-\frac{3}{2}x} +\tfrac{7}{2}e^{-\frac{1}{2}x}

    Are my answers right? . . . . Absolutely!

    Ya done real good!

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