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Question Number 206142 by universe last updated on 07/Apr/24

let \frac{d^{2} y}{{d x}^{2}} + p (x) \frac{d y}{d x} + q (x) y = 0, x \in R where

p (x) and q (x) are continuous function if

y_{1} = \sin x - 2 \cos x a n d y_{2} = 2 \sin x + \cos x

are L . I (linearly independent) solution

then ∣ 4 p (0) + 2 q (1) ∣ = ?

Answered by MaruMaru last updated on 08/Apr/24

easy

we can write more briefly like this

solution y (t) = c_{1}^{'} \sin (t) + c_{2}^{'} \cos (t)

∴ y^{(2)} (t) + y (t) = 0

y^{(2)} (t) = - c_{1}^{'} \sin (t) - c_{2}^{'} \cos (t)

y (t) = c_{1}^{'} \sin (t) + c_{2}^{'} \cos (t)

y^{(2)} (t) + y (t) = 0

∴ 2

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