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A function y=f(x) satisfies f(x) 2x+ x- (1+ 2x )f'(x)=0 with condition f(0)=0. Then, f ( 2 ) is equal to
(2) 1
dydx- 2x1+ 2x y= x1+ 2x (linear in y)
∵ ddx (1+ 2x )=- 2x ⇒ I.F. =e (1+ 2x)=1+ 2x
y (1+ 2x )= x dx=- x+C
f(0)=0 0=-1+C C=1
x= 2: f ( 2 )(1+0)=0+1 f ( 2 )=1
Answer: (2)
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