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Math Help - Differential Equation System: Laplace

  1. #1
    Newbie cith's Avatar
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    Differential Equation System: Laplace

    I want to solve this system using the Laplace transform (y_1=y_1(t),y_2=y_2(t))

    y_1=-y_1+y_2 \hspace{0.5cm} y_1(0)=0
    y_2=2y_1 \hspace{1.5cm} y_2(0)=1

    Probably not the hardest of problems, but I'm not even sure where to start :P
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  2. #2
    MHF Contributor
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    Quote Originally Posted by cith View Post
    I want to solve this system using the Laplace transform (y_1=y_1(t),y_2=y_2(t))

    y_1=-y_1+y_2 \hspace{0.5cm} y_1(0)=0
    y_2=2y_1 \hspace{1.5cm} y_2(0)=1

    Probably not the hardest of problems, but I'm not even sure where to start :P
    First I'm assuming that you have differential equations

    y'_1=-y_1+y_2 \hspace{0.5cm} y_1(0)=0
    y'_2=2y_1 \hspace{1.5cm} y_2(0)=1


    Let L(y_1) = Y_1 and L(y_2) = Y_2 so

    sY_1-0 = -Y_1 +Y_2 and sY_2 -1 = 2Y_2. Solve for Y_1 and Y_2 and then take the Laplace inverses of each.
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