There's an integral equation that I can't solve :
$$y(x) = x + \int_0^x \left(\frac{t}{x}-tx\right)y(t)\,dt+\int_x^1 \left(\frac{x}{t}-tx\right)y(t)\,dt$$
I tried differentiating it three times, but it gave me a third order differential equation that I couldn't solve.
Does anyone have a way to solve this ?
Thanks in advance