If y = f(x) satisfies the boundary value problem y" + 9y

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If y = f(x) satisfies the boundary value problem
y" + 9y = 0, y(0), y π = √2 then they π is
2 4

1. -1
2. -2
3. -3
4. -4

Correct Option: A

y" + 9y = 0
A.E. is m² + 9 = 0
m = ±3i
y = y_c + y_p
y = C₁ cos3x + C₂ sin3x
(∵ y_p = 0)
If x = 0, y = 0
0 C₁(1) + C₂(0) ⇒ C₁ = 0
If x = π/2, y = √2
√2 = C₁(0) + C₂sin(3π/2) ⇒ C₂ = - √2
∴ y = - √2 sin3x
If x = (π/4) = - √2 (3π/4) = √2(1/√2) = - 1

y" + 9y = 0, y(0), y		π		= √2 then they		π		is
		2				4