erogol
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Find all continuous functions f(x) satisfying
f(x)>1 and f(x) = x +(1 to x integral) \int f(t).dt
for all x
f(x)>1 and f(x) = x +(1 to x integral) \int f(t).dt
for all x
owlpride said:Hint: Show that f(x) has to be differentiable. Then differentiate both sides of the equation.
owlpride said:Do you mean
f(x) = x + \int_{1}^{x} f(t) dt
?
erogol said:So i did it but how can i provide the result by this way