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$y = A e^{x} + B e^{2 x} + C e^{3 x}$ satisfies the differential equation

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$y^{111} - 6 y^{11} + 11 y^{1} - 6 y = 0$

$y^{111} + 6 y^{11} + 11 y^{1} + 6 y = 0$

$y^{111} + 6 y^{11} - 11 y^{1} + 6 y = 0$

$y^{111} - 6 y^{11} - 11 y^{1} + 6 y = 0$

answer is A.

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Detailed Solution

$y_{3} - (α + β + γ) y_{2} + (α β + β γ + γ α) y_{1}$
$- (α β γ) y = 0 y_{3} - 6 y_{2} + 11 y_{1} - 6 y = 0$

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