The correct reaction involves the substitution of an alkyl halide with HI (Hydrogen iodide), which proceeds with the formation of a halide and is a typical example of nucleophilic substitution. This reaction follows Markovnikov’s addition rule where the halide (in this case, iodine) adds to the more substituted carbon of the alkyl halide.
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: