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Question

A continuous function f:RR satisfy the differential equation f(x)=(1+x2)(1+x0f2(t)1+t2dt) then the value of f(2) is

A
0
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B
1715
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C
1715
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D
1517
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Solution

The correct option is D 1517
By the fundamental theorem of calaries f is differentiate
f(x)=(1+λ2)(1+(20(f2(t)1+t2)dt))
f1(x)=2x(1+20f2(t)1+t2dt)+(1+22)(f2(x)1+x2)$
f1(x)=2x f(x)1+x2+f2(x)
This is a non linear first order differential equation
f(x)=3(x2+1)x3+3x+C,c is the whstat of
f(0)=1C=3 f(x)=3(x2+1)x33x3
f(2)=1517

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