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ecl Question 3 Suppose the roots of the auxiliary equation are as follows: mi -1, m2 = 1+2i, mz = 1 - 2i Then the general solution to the third order homogeneous differential equ constant coefficients is... y = Cie #4 Cze" sin(2x) + Cze" cos y=C: 1+ Cart y=Cje + Cye+ + Czeu y=Cje + + C2 sin(2x) + C; cos(2x) y=Cient C2. sin( 2 (In ) + C's cos(2 (In 2)).
y=Cie-* + Cyet sin(2.c) + Czet cos(2x) y=C2-' + C22 + C322 y = Cie-s + C2 et + Cze? y=Cie-+ + C, sin(2.c) + C3 cos(2x) Y = Cient + Cyz sin ( 2 (Inn)) + Caro (In )
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) + C's cos(2 (In 2)).