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Consider the differential equation: y - 5y = -2x – 4. a. Find the general solution to the corresponding homogeneous equation

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Answer #1

Jolution yl-sy = -21-4 first we will write the homogenuous equation m2 sm = 0 MCM-5)=0 m = 0, m=5 Geon + , ex Y c = c + CesYp = Ax² + BX Ypl = QAX+B Y p = DA Putting (i.) and (1) in the above differential Equation, 2A-S(2aX+6)=-24-4 2A-10AX --SB+4A= // SB = 2 +4 SB=22 A = 1/2 , B= 23 Yp = C Ax?+ BX) becomes 40={***** IY p = x ² + 224 5 y = Ye typ y = G + Cesx + x² + 2axY(x) = C + Cg esa + a2 2 + 2016 25 Y(O) = C, flg = 6 G F C q = 6 - y (M) = 8 Getat alle + dd y(o) = $(2 + dd = 1 5 SC2 = 7-216 = 897 125 y (x) = x² + 22X 5 + 153 15% + 897 125 125 2522+ 110% +18 3e8a +597 125

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