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

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$y^{'''} + 6 y^{''} - 11 y^{'} + 6 y = 0$

$\begin{aligned} y^{'''} + 6 y^{''} + 11 y^{'} + 6 y = 0 \end{aligned}$

$\begin{aligned} y^{'''} - 6 y^{''} + 11 y^{'} - 6 y = 0 \end{aligned}$

$y^{'''} - 6 y^{''} - 11 y^{'} + 6 y = 0$

answer is A.

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Detailed Solution

$y = A e^{x} + B e^{2 x} + C e^{3 x}$

Required differential equation is $(D - 1) (D - 2) (D - 3) y = 0 \Rightarrow (D^{3} - 6 D^{2} + 11 D - 6) y = 0$

$\Rightarrow \begin{aligned} y^{'''} - 6 y^{''} + 11 y^{'} - 6 y = 0 \end{aligned}$

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