Should I apply boundary conditions in the general solution before finding the particular solution? Given a function:
$$ y'' - y' = x$$ I want to find the solution where $x = 1$, $y = 1$, $dy/dx = 2$.
I have managed to find the full form of the equation by first finding the complementary function solution and then the particular solution.
The problem is if I apply the boundary conditions after I find the complementary function solution, I get a different answer than applying after I find the full solution $y = y_c + y_p$, where $y_c$ is the complementary one and $y_p$ is the particular solution.
When should I apply the boundary conditions?

You should apply the boundary conditions to the general solution that you have already determined: 
$$y(x)=\underbrace{C_1+C_2e^x}_{y_o}+\underbrace{-\frac{x^2}{2}-x}_{y_p}.$$
So it remains to find $C_1$ and $C_2$ such that $y(1)=1$ and $y'(1)=2$.
