General Solution of inhomogenous ODE

ok,so again, reading my lecture notes,i bumped into this problem..

consider

A = (1 2,

0 -1)

find the general solution of

__x__' = A__x__ + ( 0,1 )

write __x__ = (x, y) then the ODE is :

x' = x+2y

y' = -y + 1

y' = -y+1 implies y(t) = Ce^-t + 1 (how did one obtain this?? )

The ODE for x(t) is x' = x + 2(C(e^-t) + 1)

This linear inhomogeneous ODE gives x(t) = -2 - c(e^-t) + d(e^t) again how does one get this? i integrated but i cant get this. after trying for hours..i simply gave up ='(

thank you !