Differential equation with an integral I need to find function $f$ (the book doesn't specify whether $f(x)$ or $f(t)$) that satisfies the following equation:
$$\int_0^xf(t)\,dt= {2 \over 3}xf(x)$$
Can anyone please tell me how this problem can be solved?
I would be very grateful!

Hint: Differentiate the equation (why can you differentiate the RHS?) to get an ordinary differential equation. Use the fundamental theorem of calculus to differentiate the LHS.
