(1 point) Consider the following initial value problem: 64y=lỗi y” +64y: 2t, 0≤t <2 0, t> 2 y(0) = 0, y'(0) = Using Y fo

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(1 point) Consider the following initial value problem: 64y=lỗi y” +64y: 2t, 0≤t <2 0, t> 2 y(0) = 0, y'(0) = Using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s) = -4((e^(-2s))/s(s^2+64))-2(e^(-2s)/(s^2(s^2+64))).

(1 point) Find the Laplace transform of 0, 5 sin(at), 0, F(s) = f(t) = t<4 4 < t < 5 t≥ 5