Given the fourth order homogeneous constant coefficient equation y'''' + 13y'' + 36y = 0
a)the auxiliary equation is⁴ + br³ + cr² + dr + e = 0.
b)The roots of the auxiliary equation are -2i, 2i, -3i, 3i (enter answers as a comma separated list).
c)A fundamental set of solutions is (Enter the fundamental set as a commas separated list yₗ, y₂, y₃, y₄).
Therefore the general solution can be written as y = c₁y₁ + c₂y₂ + c₃y₃ + c₄y₄.
d)Use this to solve the IVP with y (0) = 1, y' = -3, y''(0) = -14, y"'(0) = 27 y(x) =