Differential Equations

Let $f(x)$ be a continuously differentiable function on the interval $(0, \infty)$ such that $f(1)=2$ and

\(\lim\limits_{t \rightarrow x} \frac{t^{10} f(x)-x^{10} f(t)}{t^9-x^9}=1\)

for each $x>0$. Then, for all $x>0, f(x)$ is equal to :