Differential Equations Help
Here's the question:
dY/dt = (-2 1;0 2) * Y, where the first row of the matrix is [-2 1] and the second row is [0 2].
(a) Show that (0,0) is a saddle.
(b) Find the eigenvalues and eigenvectors and sketch the phase plane.
(c) On the phase plane, sketch the solution curves with initial conditions (1,0.01)
and (1,-0.01).
(d) Estimate the time t at which the solutions with initial conditions (1,0.01) and (1,-0.01) will be 1 unit apart.
My answers are correct for parts a through c:
Eigenvalues are -2 and 2, since they have opposite signs we have a saddle at the origin. Eigenvectors are <1,0> and <1,4>. My phase plane sketch is also correct, however I have no idea how to do part d. Answer is supposedly t=1.96seconds. Thanks!
7 Comments • Newest first
[quote=ShammyShakes]I really don't know what the question is asking. I'm assuming I should find two particular solutions for the given initial conditions, but then what? How do I go about finding the distance between them?
@NonSonoFronz I took a brief linear algebra course last semester so I'm familiar with the terminology, yeah.[/quote]
So you have the two Y1(t) and Y2(t) with the two initial conditions, and the question is probably asking for the time t=T where the magnitude of Y1(T)-Y2(T) is equal to 1.
[quote=cb000]So...are you stuck figuring out the particular solutions with those initial conditions?[/quote]
I really don't know what the question is asking. I'm assuming I should find two particular solutions for the given initial conditions, but then what? How do I go about finding the distance between them?
@NonSonoFronz I took a brief linear algebra course last semester so I'm familiar with the terminology, yeah.
So...are you stuck figuring out the particular solutions with those initial conditions?
In your diff eq class did you go over vector spaces, subspaces, dimensions, null spaces, etc.?
This ish is easy af idk why this problem is giving me such a hard time
I'm lost.
i'm so glad i'm not taking this class