How to break a second order differential equation to 2 1st order differential equations? for example y'' + 2y' + 2y = 0

Question

anonymous · Answer

the answer is y'= z and z'=-2z-2y, but i have no idea how it come to that

ganeshie8 · Answer

say   $z = y'   $

$\implies  z' =    y''$

ganeshie8 · Answer

solve y'' from the given equation and plug it above

anonymous · Answer

what do you mean? i need to solve the 2nd differential eqn first?

ganeshie8 · Answer

sorry i meant just to isolate y'', like below :

y'' + 2y' + 2y = 0

=>   y'' =  -2y' - 2y

anonymous · Answer

ohhh! now i get it! haha thanks! :D btw do u know how to draw phase portrait of those eqns? i wanna know how to be able to draw it ):

ganeshie8 · Answer

no clue on that sorry :(

anonymous · Answer

okay thanks anw! :D