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A function f: RvecR satisfies xcosy(f(2x...

A function `f: RvecR` satisfies `xcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+2y)+f(2x-2y))dot` If `f^(prime)(0)=1/2,t h e n` `a)f^(prime)(x)=f(x)=0` `b)4f^(x)+f(x)=0` `c)f^(x)+f(x)=0` `d)4f^(x)-f(x)=0`

A

`f(x)''(x)=f(x)=0`

B

`4f''(x)+f(x)=0`

C

`f''(x)+f(x)=0`

D

`4f''(x)-f(x)=0`

Text Solution

Verified by Experts

The correct Answer is:
B
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