Consider the differential equation y" - 7 y' +10y = -5 e³t. (a) Find r₁, 2, roots of the characteristic polynomial of the equation above. 11, 12 = (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. y₁ (t) = y₂ (t) = (c) Find a particular solution yp of the differential equation above. Yp (t) = (d) Find the solution y of the the differential equation above that satisfies the initial conditions y(0) = 2, y(t) = y' (0) = -4. Σ M M M M

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