Answer:
Explanation:
The characteristic equation of the given differential equation is:
r^3 - 4r^2 - 5r = r(r^2 - 4r - 5) = r(r - 5)(r + 1) = 0
Thus, the roots of the characteristic equation are r = 0, r = 5, and r = -1.
Therefore, the general solution of the differential equation is:
y(t) = c1 e^(0t) + c2 e^(5t) + c3 e^(-t)
Simplifying this expression, we get:
y(t) = c1 + c2 e^(5t) + c3 e^(-t)
where c1, c2, and c3 are constants determined by the initial conditions of the problem.