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2) A function f:R->R satisfies sinx 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) =0 b) 4f''(x) + f(x) =0 c) f''(x) + f(x) =0 d) 4f''(x) - f(x) =0

2) A function f:R->R satisfies 
  sinx 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) =0
  b) 4f''(x) + f(x) =0
  c) f''(x) + f(x) =0
  d) 4f''(x) - f(x) =0

Grade:12

1 Answers

Sourabh Singh IIT Patna
askIITians Faculty 2104 Points
7 years ago
Use substitution to convert

2x-2y into a single variable

2x+2y into a single variable..


from there use property of Cos n Sine of multiple angles to find out the asked relation of the function given in the options

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