1. ## calculus problem

Find f(x) if f is continuous for x>0 and (f(x))^2 = (integral of f(t) dt from 0 to x) + 9

2. Originally Posted by Susie38
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:

Find $f(x)$ if $f$ is continuous for $x>0$,
and:

$(f(x))^2=\int_0^x f(t) dt$.

If you differentiate this last equation you get:

$2f(x)\frac{df}{dx}=f(x)$,

which is an ODE which you should be able to solve
(though you may have to take extra care about points
where $f(x)=0$).

RonL

3. what is ode?

4. Originally Posted by Susie38
what is ode?
Ordinary Differential Equation.

RonL