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KCET2013MathematicsDifferential Equations

If f(x) is a function such that f^ (x)+f(x)=0 and g(x)=[f(x)]²+ [f^ (x) ]² and g(3)=8 , then g(8) is equal to

Options

  1. A0
  2. B3
  3. C5
  4. D8

Correct answer

D. 8

Step-by-step solution

Given, f^ (x)+f(x)=0...(i) and g(x)=[f(x)]²+ [f^ (x) ]² Now, on differentiating w.r.t. x , we get g^ (x)=2 f(x) f^ (x)+2 f^ (x) f^ (x)=2 f(x) f^ (x)+2 f^ (x) -f(x) [from Eq. (i)] =2 f(x) f^ (x)-2 f^ (x) f(x)=0 array ll & g(x)= constant & g(3)=8 & g(8)=8 (given) array

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