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?