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kailoon889 Group Title

Use Laplace transform to solve the following system: x''=x+3y y''=4x-(4e^t) x(0)=2; x'(0)=3 ;y(0)=1 ;y'(0)=2

  • 2 years ago
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  1. TuringTest Group Title
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    Laplace to solve a system? new one on me, can't wait to see the soution

    • 2 years ago
  2. TuringTest Group Title
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    ...but you know how to take the laplace of these expressions, right?

    • 2 years ago
  3. kailoon889 Group Title
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    yeah but i have no idea how to solve this system D=

    • 2 years ago
  4. TuringTest Group Title
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    me neither :( let me call for reinforcements: @JamesJ @Mr.Math @across @lalaly help with a DE system

    • 2 years ago
  5. exraven Group Title
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    transform both DEs\[s^{2} X(s) - sx(0) - x'(0) = X(s) + 3Y(s)\]\[s^{2}Y(s) - sy(0) - y'(0) = 4X(s)-\frac{4}{s-1}\]plug in the initial conditions, simplify and solve for X(s) and Y(s)

    • 2 years ago
  6. Mr.Math Group Title
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    It's easy if you already know how to do the laplace transform. You'll be left, as exraven explained, with two equations in two variables \(X(s)\) and \(Y(s)\), solve for them and then take the inverse laplace transform to each one separately.

    • 2 years ago
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