Question

rivete general solutions ts ar Followa elifFerential hese geralsoluhoatto solve nbal vale problem Rquahons and use the 20 y (37

Answer 1

Therefore c_2 + 16x (-2) = -37 (from (c)) c_2 - 32 = -37 c_2 = -37 + 32 c_2 = -5 therefore c_1 - 5 - 2 = 1 (from (A)) c_1 = 1 + 7 c_1 = 8 Hence y(x) = 8 + (-5)e^x + (-2)e^-4x y(x) = 8 - 5e^x - 2e^-4x. Ans \r\n (a) Y^'' + 9Y^' + 14Y = 0 equation (1) y(0) = 5, y^'(0) = -25 A.E of (1) is m^2 + 9m + 14 = 0 m^2 + 7m + 2m + 14 = 0 m(m - 7) + 2(m + 7) = 0 (m + 2) (m + 7) = 0 m = -2, -7 therefore y(x) = c_1e^-2x + c_2 e^-7x y(0) = 5 y^'(0) = -25 c_1 + c_2 = 5 equation (A) implies -2 c_1 e^-2x - 7c_2 e^-7x = -25 -2c_1 -7c_2 = -25 equation (B) multiplying (A) by 2 and add with (B) 2c_2 - 7c_2 = 10 - 25 -5c_2 = -15 c_2 = 3 therefore c_1