• Math Archive: Questions from 2023-02-23

    f(t) = {0, 0 <= t < 1 t^2, t >= 1 Write the function in terms of unit step functions. Find the Laplace transform of the given function. F(s) =

    1 answer

    f(t) = {t, 0 <= t < 5 0, t >= 5 Write the function in terms of unit step functions. Find the Laplace transform of the given function. F(s) =

    1 answer

    Use the Laplace transform to solve the given initial-value problem. y' + y = f(t), y(0) = 0, where f(t) = {0, 0 <= t < 1 8, t >= 1 y(t) =

    1 answer

    Use the Laplace transform to solve the given initial-value problem. y' + y = f(t), y(0) = 0, where f(t) = {1, 0 <= t < 1 -1, t >= 1 y(t) =
    1 answer

    Use the Laplace transform to solve the given initial-value problem. y' + 3y = f(t), y(0) = 0, where f(t) = {t, 0 <= t < 1 0, t >= 1 y(t) =
    1 answer

    Consider the following initial-value problem. y' + 4y = f(t), y(0) = 0, where f(t) = {t, 0 <= t < 1 0, t >= 1 Write the function f(t) in terms of unit step functions. Find the Laplace transform of the given function. F(s) = Use the Laplace transform to solve the given initial-value problem. y(t) =
    1 answer

    Use the Laplace transform to solve the given initial-value problem. y'' + 4y = sin(t) u(t - 2pi), y(0) = 1, y'(0) = 0 y(t) =

    1 answer

    Use the Laplace transform to solve the given initial-value problem. y'' - 9y' + 20y = u(t-1), y(0) = 0, y'(0) = 1

    1 answer

    y" + y = f(t), y(0) = 0, y'(0) = 1, where f(t) = {0, 0 <= t < pi 1, pi < = t < 2pi 0, t >= 2pi Use the Laplace transform to solve the given initial value problem. y(t) =

    1 answer

    Use the improved Euler’s method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. y’ = 4x – 3y + 3, y(1) = 4; y(1.5) h = 0.1 y(1.5) h = 0.05 y(1.5)
    1 answer