ok,so again, reading my lecture notes,i bumped into this problem..
A = (1 2,find the general solution of
x' = Ax + ( 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 !