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kailoon889

  • 2 years ago

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

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

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

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

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

  5. exraven
    • 2 years ago
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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)

  6. Mr.Math
    • 2 years ago
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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.

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