We know:
\[ r = 0.529 \frac{n^2}{Z} \implies 8.48 = 0.529 \frac{n^2}{1} \]
\[ n^2 = 16 \implies n = 4 \]
We also know:
\[ E \propto \frac{1}{n^2} \]
\[ E_n = \frac{E}{16} \]
Thus, $x = 16$.
If \[ \frac{dy}{dx} + 2y \sec^2 x = 2 \sec^2 x + 3 \tan x \cdot \sec^2 x \] and
and \( f(0) = \frac{5}{4} \), then the value of \[ 12 \left( y \left( \frac{\pi}{4} \right) - \frac{1}{e^2} \right) \] equals to: