Let f:(0, ) be a function which is differentiable at all points of its domain and satisfies the condition x2f'(x)=2xf(x)+3, with f(1)=4. Then 2f(2) is equal to :
(4) 39
x2f'-2xf is the numerator of the quotient rule, so divide by x4:
ddx ( fx2 )= 3x4 fx2=- 1x3+C
f(1)=4 4=-1+C C=5
f(x)=- 1x+5x2 f(2)= 392
2f(2)=39
Answer: (4)
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