Hey, i got a few questions

sorry

1 - I haven't come across the term "Bump Up" in all my notes and texts, can you explain?

2 -WELL I've tried to do it again, here's what I've got. PLEASE tell me where I've gone WRONG

$\displaystyle \frac{d^2y}{dx^2} + \frac{dy}{dx} - 2y = 0$

The characteristic equation: $\displaystyle m^2 + m - 2 = 0$

The roots to this equation: $\displaystyle m_1 = -2$ and $\displaystyle m_2 = 1$

therefore the complementary function: $\displaystyle x(t) = Ae^{-2t} + Be^{t}$

Mr F says: Correct in spirit I suppose. But shouldn't it be $\displaystyle {\color{red}y(x) = Ae^{-2x} + Be^{x}}$ ....
so my $\displaystyle y_p(x) = \frac{-2}{-3}xe^{-2x}$

Mr F says: This part is correct. But there's another part that you've forgotten to include. See main reply below.
therefore my general solution is $\displaystyle y(x) = \frac{2}{3}xe^{-2x} - Ae^{-2t} + Be^{t}$

Thanks again