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y(x) = 3 x e 2x year = 302X -27 6x222 Y"(x) = -6e2x 6 e 20 + 12ne = -12724 +12272x ->_-443724_6*821) — 120€ y"Q)= – 4 Y'(31) – 4 y(2 y"63 +4 y' () + 4 9122=0 This is required second-ordles differential Equation. Giren 9, 601) = asina Wronskian of y, and and y (n) = (05x is Why 1/2) 1 x sinx - losa Here - sjon +*(osa -sinn = -xsin't - sinn a losx Wly, 192) = -x-sina WIB,192) to Y, are linearly independent --Solution P
ya) = sina Hytutt Here yol is bounded for all afir y'(n) = COS y"fatta-sını y" com =-4( Y"621) + 46011 = 0 This is This is roauired required second order ODF.
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