Hey, for this System I want to find the general solution but $\displaystyle y_1 '$ and $\displaystyle y_2 '$ both have constants which I can't remember how to deal with.

Find the general solution to:

$\displaystyle y_1 ' =-y_1 +2$

$\displaystyle y_2 ' = -y_2 -1$

And I have a non-linear system that needs to be linearised but my working is getting me nowhere.

Linearise the system around the critical point (0,0):

$\displaystyle \frac{dx}{dt}=1-e^{x+y}$

$\displaystyle \frac{dy}{dt}=2x+sin(y)$

Any help would be greatly appreciated.

Thanks