Question

$\lim_{t \rightarrow x}\mspace{2mu}\frac{2tf(x) - x^{2}f'(t)}{- 1} = 3$

$${x^{2}f'(x) - 2xf(x) = 3 }{\frac{dy}{dx} - \frac{2y}{x} = \frac{3}{x^{2}} }$$I.F. $= e^{- \int\frac{2}{x}dx} = e^{- 2\log_{e}x} = 1/x^{2}$

$${y \cdot \frac{1}{x^{2}} = \int\frac{3}{x^{4}}dx }{\frac{y}{x^{2}} = - \frac{1}{x^{3}} + c \Rightarrow y = cx^{2} - \frac{1}{x} = f(x) }{f(1) = 2 = c - 1 \Rightarrow c = 3 }{f(x) = 3x^{2} - \frac{1}{x} }{f(2) = 12 - \frac{1}{2} \Rightarrow 2f(2) = 23}$$