It is given that y + 2 y' = 0, y = 0, y(0) = 0, y(1)= 0.

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It is given that y + 2 y' = 0, y = 0, y(0) = 0, y(1)= 0. What is y(0.5)?

1. 0
2. 0.37
3. 0.62
4. 1.13

Correct Option: A

y" + 2y' + y = 0
A.E is, D² + 2D + 1 = 0
⇒ (D + 1)² = 0
⇒ m = – 1
The C.F. is (C₁ + C₂ x)e^–x and P.I. = 0
Now y(0) = 0
⇒ C₁ = 0 a
nd y(1) = 0
⇒ C₂ e^–1 = 0,
⇒ C₂ = 0
⇒ C.F. = 0
⇒ y(0.5) = 0