Question

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

Answer 1

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

Answer 2

say \(z = y' \)

\(\implies z' = y''\)

Answer 3

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

Answer 4

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

Answer 5

sorry i meant just to isolate y'', like below :

y'' + 2y' + 2y = 0

=> y'' = -2y' - 2y

Answer 6

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 ):

Answer 7

no clue on that sorry :(

Answer 8

okay thanks anw! :D