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Let f, g : [-1, 1] → R, f (x) = x3, g(x) = x2 IxI Then
y" + py' + qy = 0 on [-1, 1]
  • a)
    f and g are linearly independent on [-1,1]
  • b)
    f and g are linearly dependent on [-1, 1]
  • c)
    f(x) g(x) - f(x) g (x) is NOT Identically zero on [-1, 1]
  • d)
    There exist continuous function pix) and q(x) such that/ and g satisfy
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Let f, g : [-1, 1] → R, f (x) = x3, g(x) = x2 IxI Theny" + p...
Here, lxI = -x for x < 0 = x for x ≥ 0
So, g(x) = x3 for x ≥ 0 
= -x3 for x < 0 
and f(x) = x3
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Let f, g : [-1, 1] → R, f (x) = x3, g(x) = x2 IxI Theny" + p...
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Let f, g : [-1, 1] → R, f (x) = x3, g(x) = x2 IxI Theny" + p...
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Let f, g : [-1, 1] → R, f (x) = x3, g(x) = x2 IxI Theny" + py' + qy = 0 on [-1, 1]a)f and g are linearly independent on [-1,1]b)f and g are linearly dependent on [-1, 1]c)f(x) g(x) - f(x) g (x) is NOT Identically zero on [-1, 1]d)There exist continuous function pix) and q(x) such that/ and g satisfyCorrect answer is option 'B'. Can you explain this answer?
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