• Math Archive: Questions from 2023-03-25

    y' - 3y = del(t - 5), y(0) = 0 Use the Laplace transform to solve the given initial-value problem.

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    y' + y = del(t - 1), y(0) = 4 Use the Laplace transform to solve the given initial-value problem.

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    y'' + y = del(t - 2pi), y(0) = 0, y'(0) = 1 Use the Laplace transform to solve the given initial-value problem.

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    y'' + y = del(t - pi/2) + del(t - 3pi/2), y(0) = 0, y'(0) = 0 Use the Laplace transform to solve the given initial-value problem.

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    y'' + y = del(t - 6pi) + del(t - 8pi), y(0) = 1, y'(0) = 0 Use the Laplace transform to solve the given initial-value problem.

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    y'' + 3y' = del(t - 1), y(0) = 0, y'(0) = 1 Use the Laplace transform to solve the given initial-value problem.

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    dx/dt = -x + y dy/dt = 2x x(0) = 0, y(0) = 9 Use the Laplace transform to solve the given system of differential equations.

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    dx/dt = 3y + e^t dy/dt = 12x - t x(0) = 1, y(0) = 1 Use the Laplace transform to solve the given system of differential equations.

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    dx/dt = x - 2y dy/dt = 5x - y x(0) = -1, y(0) = 5 Use the Laplace transform to solve the given system of differential equations.

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    dx/dt + 3x + dy/dt = 1 dx/dt - x + dy/dt - y = e^t x(0) = 0, y(0) = 0 Use the Laplace transform to solve the given system of differential equations.

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    2dx/dt + dy/dt - 2x = 1 dx/dt + dy/dt - 5x - 5y = 2 x(0) = 0, y(0) = 0 Use the Laplace transform to solve the given system of differential equations.

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    d^2x/dt^2 + x - y = 0 d^2y/dt^2 + y - x = 0 x(0) = 0, x'(0) = -3, y(0) = 0, y'(0) = 1 Use the Laplace transform to solve the given system of differential equations.

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    dx/dt = 4x - 2y + 2u(t-1) dy/dt = 3x - y + u(t-1) x(0) = 0, y(0) = 1/6 Use the Laplace transform to solve the given system of differential equations.

    1 answer