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Solve the differential equation by variation of parameters. Y + 3y + 2y = 6 > 9+ et

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Sol? 9 + 3y + 2y = 4+ex (D*+ 30+2)} = gtext , where Daten Auseilasy equation is per a (m+i) (m+2) = 0 => m= -1,-2 Complement{ variation of parameter: Consider the differential equation y + 90) y + 8(x) y = g(5), whese 9682, 8(be) and goes are func. Now, Let = 8-23 us assume ume Y, (%) = e-x, Ya(x) = 6-2. So, y() = -eX & (a) = -26-2* W($1,da) = (2+*)(-24-28) - (-20) (Now, put ate?=m, then el dx = dm . So, station en pel te} Se hele ak = d m = Inpol They Sen | 94e447 ex iex 9tex . put 9+et=nSo, the general solution of given differential equation (say ) is y = Ye + IP y = ge-* + G 1-2x + (9 1-2x + (-x) In/e%+91- e-

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