differential!!!

$\textbf{The general solution =compimentary function, C.F + particular integral, P.I}$ To calculate the C.F, $\frac{d^2y}{d^2x}-\frac{dy}{dx}-2y= 0$
$m^2 - m -2=0$ $m= 2,m= -1$ The solution of C.F = $Ae^{m_1x} + Be^{m_2x}$ = $Ae^{2x} + Be^{-x}$

To solve Particular integral, P.I on the R.H.S of the equation , y=8, we substitute the 8 with a constant c, therefore, $\frac{dy}{dx}= 0$ , $\frac{d^2y}{d^2x}=0$ substitute the value of $\frac{dy}{dx}= 0$ and $\frac{d^2y}{d^2x}=0$ into the real equation, therefore, 0 - 0 - 2y = $8$ y = $-4$ General solution = $C.F + P.I$ = $Ae^{2x} + Be^{-x} -4$