Solve a 5th order linear homogeneous differential equation with constant coefficients:
y⁵ - y⁴ + 8y³ + 10y'' = 0.
a) y(x) = c1eˣ + c2e(2x) + c3e(3x) + c4e(-2x) + c5e(-5x)
b) y(x) = c1e(2x) + c2e(3x) + c3e(4x) + c4e(-x) + c5e(-2x)
c) y(x) = c1e(2x) + c2e(3x) + c3e(-2x) + c4e(-3x) + c5e(-4x)
d) y(x) = c1e(3x) + c2e(4x) + c3e(5x) + c4e(-3x) + c5e(-4x)