Asked by bob
Find a function f which satisfies the integral equation
Int(bounded from 0 to x) t*f(t)dt = Int(bounded from x to 0)(t^2+1)*f(t)dt +x
Int(bounded from 0 to x) t*f(t)dt = Int(bounded from x to 0)(t^2+1)*f(t)dt +x
Answers
Answered by
Mgraph
Differentiating the equation:
x*f(x)=-(x^2+1)*f(x)+1
f(x)=1/(x^2+x+1)
x*f(x)=-(x^2+1)*f(x)+1
f(x)=1/(x^2+x+1)
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