The general solution of the differential equation $(D^{2} - 4 D + 4) y = 0$ is of the form $(g i v e n D = \frac{d}{d x} a n d C_{1}, C_{2} a r e c o n s t a n t s)$

C_{1} e^{2 x}

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C_{1} e^{2 x} + C_{2} e^{- 2 x}

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C_{1} e^{2 x} + C_{2} e^{2 x}

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C_{1} e^{2 x} + C_{2} x e^{2 x}

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Solution

The correct option is D $C_{1} e^{2 x} + C_{2} x e^{2 x}$
$(D^{2} - 4 D + 4) y = 0$ .... (i)
AE is $m^{2} - 4 m + 4 = 0$
$m = 2, 2$
So, solution is $y = (C_{1} + C_{2} x) e^{2 x}$

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