2) A function f:R->R satisfiessinx cosy (f(2x+2y) - f(2x-2y)) = cosx siny (f(2x+2y) + f(2x-2y)).If f'(0)=1/2, then: a) f''(x) - f'(x) =0b) 4f''(x) + f(x) =0c) f''(x) + f(x) =0d) 4f''(x) - f(x) =0

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Sum of series 2[n/2] ! [n/2]!/ n! [2Co-2C2+3C2....+[-1]^n[n+1]2Cn] where n is an even positive integer. Kindly provide solution of this question and how to generalise this. How do we know that which expansion will give this?

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