Find f(x) if f is continuous for x>0 and (f(x))^2 = (integral of f(t) dt from 0 to x) + 9
The question is:Originally Posted by Susie38
Find $\displaystyle f(x)$ if $\displaystyle f$ is continuous for $\displaystyle x>0$,
and:
$\displaystyle (f(x))^2=\int_0^x f(t) dt$.
If you differentiate this last equation you get:
$\displaystyle 2f(x)\frac{df}{dx}=f(x)$,
which is an ODE which you should be able to solve
(though you may have to take extra care about points
where $\displaystyle f(x)=0$).
RonL