Limits Continuity And Differentiability

Let \(f\) be a differentiable function in the interval \((0, \infty)\) such that \(f(1)=1\) and \(\lim _\limits{t \rightarrow x} \frac{t^2 f(x)-x^2 f(t)}{t-x}=1\) for each \(x>0\). Then \(2 f(2)+3 f(3)\) is equal to _________.