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Find two linearly independent solutions of the 2nd-order linear homogeneous differential equation 3; ly' 30;; = U The linearly independent solutions are and the general

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Find two linearly independent solutions of the 2nd-order linear homogeneous differential equation 3;\" ly' 30;; = U The linearly independent solutions are and the general solution of the equation is yl-r) = @ where "1- and "2 are arbitrary constants. (Note:Let ml and 1112 be two solutions of the auxiliary (characteristic) equation. (i) If \"'1 '4 \"'2, write Ill : "ml: and Hz = "my; (ii) If \"'1 = \"12, write Ill = "m\" and 92 = Jim\"; and (iii) If m1 = a. + bi! and \"12 = o In" write 1;] = t'\" (\"US [burl and y? = ("H Sill lib-37),)

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