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Most Important Selected Qs for JEE AdvancedMathematicsDifferential Equations

A function f : R R satisfies 2 x 2 y f(3 x+3 y)+f(3 x-3 y) = 2 x 2 y f(3 x-3 y)-f(3 x+3 y) ; if f(0)=1 then

Options

  1. A4 f(x)+9 f^ (x)=0
  2. Bf(x)+f^ (x)=0
  3. C4 f(x) ^2+9 f(x) ^2=4
  4. D9 f(x) ^2+4 f(x) ^2=4

Correct answer

C. 4 f(x) ^2+9 f(x) ^2=4

Step-by-step solution

2 x 2 y f(3 x+3 y)+f(3 x-3 y) = 2 x 2 y f(3 x-3 y)-f(3 x+3 y) (f 3 x+3 y) (2 x-2 y)=f(3 x-3 y) (2 x+2 y) f(3 x+3 y) f(3 x-3 y) = (2 x+2 y) (2 x-2 y) f(3 x+3 y) (2 x+2 y) = f(3 x-3 y) (2 x-2 y) f( ) ( 2 3 ) = f( ) ( 2 3 ) =k f(x)=k ( 2 x 3 ) f ( x )= ( 2 x 3 ) (1) f(0)=1]f^ (x)=- 2 3 ( 2 x 3 ) .....(ii) f^ (x)=- 4 9 ( 2 x 3 ) ....(iii)

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