Consider the differential equation 3y"(x) + 27y(x) = 0 with

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Consider the differential equation 3y"(x) + 27y(x) = 0 with initial conditions y(0) and y'(0) = 2000. The value of y at x = 1 is _________.

1. 94.08
2. 95
3. 94.58
4. 94

Correct Option: A

The D.E. is 3y (x) + 27 y (x) = 0
The auxiliary equation is
3 m² + 27 = 0 m² + 9 = 0
m = ≠ 3i Solution is y = C₁ cos 3x + C₂ sin 3x
Given that y (0) = 0
∴ 0 = C₁
y' = –3 C₁. sin 3x + 3 c₂ cos 3x
y' (0) = 2000
2000 = 0 + 3 C₂

C₂ =	2000
	3

∴ Solution is

y =	2000	sin 3x
	3

when x = 1, y =	2000	sin 3 = 94.08
	3