Consider the differential equation y 4y' + 3 y = -2 et. (a) Find r1,...

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Consider the differential equation y" – 4y' + 3 y = -2 et. (a) Find r1, r2, roots of the characteristic polynomial of the equation above. T1, 72 1,3 Σ (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. Y1 (t) Σ e^t Y2(t) = e^(3t) (C) Find a particular solution y, of the differential equation above. Yp(t) = | 2e^(21) Σ (d) Find the solution y of the the differential equation above that satisfies the initial conditions y(0) = -2, 3/ (0) = -4. y(t) = 2e^(2t)-4t Σ Consider the differential equation y" – 4y' + 3 y = -2 et. (a) Find r1, r2, roots of the characteristic polynomial of the equation above. T1, 72 1,3 Σ (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. Y1 (t) Σ e^t Y2(t) = e^(3t) (C) Find a particular solution y, of the differential equation above. Yp(t) = | 2e^(21) Σ (d) Find the solution y of the the differential equation above that satisfies the initial conditions y(0) = -2, 3/ (0) = -4. y(t) = 2e^(2t)-4t Σ