Find the solution of the differential equation y ^ (4) + y '' '+ y' + y = 0,

Typical linear homogeneous equation with constant coefficients: characteristic equation: R ^ 4 + R ^ 3 + R + 1 = 0r ^ 3 (R + 1) + R + 1 = 0 (R + 1) (R ^ 3 + 1) = 0 (R + 1) (R + 1) (R ^ 2-r + 1) = 0r1 = - 1 R2 = - 1 R3 = 1 / 2 + I root 3 / 2 R4 = 1 / 2-I root 3 / 2 the general solution is: y = (c1x + C2) e ^ (- x) + {c3cos [(root 3) x / 2] + c4sin [(root 3) x / 2]} e ^ (

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