Final answer:
The general solution of the given differential equation is y(x) = c1e^-x + c2e^((-1-2i)x) + c3e^((-1+2i)x), where c1, c2, and c3 are constants.
Step-by-step explanation:
In order to find the general solution for the given differential equation y'''+ y'' + 3y' - 5y = 0, we can assume that the solution can be written as y = erx. By substituting this assumption into the equation, we get a characteristic equation r3 + r2 + 3r - 5 = 0. By solving this equation, we find the roots r1 = -1, r2 = -1 - 2i, and r3 = -1 + 2i.
Therefore, the general solution is given by:
y(x) = c1e-x + c2e(-1-2i)x + c3e(-1+2i)x
where c1, c2, and c3 are constants determined by the initial conditions of the problem.