Equilibrium Points

[mooshupork34]

The functions A(t) and B(t) are solutions to this system of differential equations:

x' = y
y' = x
x(0) = 1
y(0) = 0

Find and classify all equilibrium points of this system.

 

[Steem]

x' = y
y' = x
x(0) = 1
y(0) = 0

Find and classify all equilibrium points of this system.

If you use operators than you could solve for x or y.

x'-y=0
(D)[y']-(D)x=(D)[0]

add the two together and end up with y''-y=0.

solve for y(t) and you know that x(t) is equal to y'(t) for your inital conditions. the equilibrium points are when you solutions are equal to zero.

Hope this helps!