Recent content by the7joker7

For the most part, I understand the relationship between behavior and eigenvalues. When you have two positive eigenvalues it's a source, two negative it's a sink, so on and so forth... My issue is, what's the easiest way to find for which values of A and B are there complex values involved.

Homework Statement Basically, the problem involves a linear system dx/dt = ax + by and dy/dt = -x - y, with a and b being parameters that can take on any real value. Basically, you go through this system for several values of a and b (I did -12 to 12) to find the state at various points...

Homework Statement I have two large parallel plates that are conducting and separated by 10.0cm. The charges on the plates are uniform and equal in magnitude but opposite in sign. The difference in potential between the two is 500 V. The first question concerning this is which plate...

Homework Statement Basically, I have a differential equation. One of the elements of it is... F(P) = 0.2P(1 - (P/10)) And I need to replace it with it's first-order Taylor polynomial centered at P=10. The Attempt at a Solution I haven't done Taylor polynomial stuff in over a...

y dy = (t dt)/(t^2 + 1) y^2/2 = (t dt/t^2) + t dt (If I understand correctly, this is separating?) y^2/2 = ((t^2)/2)/t^2 + t^2/2 y^2/2 = 1/2 + t^2/2 y^2 = 1/4 + t^2/4 y = sqrt(k(.25 + t^2/4)) Eh?

Lesse dy/dt = t/((t^2)y + y) dy/y = t/((t^2)y^2 + y^2) dt dy/y * y^2 + y^2 = t/(t^2) dt dy/y * 2(y^2) = 1/t ln(y) * 2(y^3/3) = 1/t Ugh...I dunno, something in that ballpark? I'm confused...

Oops, my bad. It's the 2nd one. dy/dt = t/((t^2)y + y)

Just to be sure, is the basic starting step for all problems of this type getting dy/y? Like if I have the same question with dy/dt = t/(t^2y + y), I would try to get dy/y on one side?

log(y) = t^2/2 So y = e^(t^2/2) Alright. And the k is because it's a general equation and k needs to be there so it can be solved for any initial condition. But why is the k being multiplied and not added?

dy/y = t dt The integral of that would be... dy = t^2/2 So (t^2/2)/dt = ty t^2/2 = ty dt Where do I go from here?

Homework Statement Find the general solution of the differential equation specified. \frac{dy}{dt} = ty. The Attempt at a Solution I already know the answer to be ke^{t^{2}/2}, but can't figure out how it got here. I'm rusty with my integrals and am just really starting diff eqs...

Lemme see here... The series is indeed telescoping and I have it simplifying to... ((2^k)/k!) - (((n + 2)/(n + 1))^k)/k! Since n + 2 over n + 1 will run to 1... ((2^k/k!) - ((1^k/k!)) So... 1^k/k! Am I on the right track?

Ohhh...I see. So, what is k supposed to be? Is it just a variable, or does it get a value?

Very close! But, alas, putting numbers in for n for the first three terms gives... (2 - 1.5) + (1.125 - .88889) + (.39506 - .3255208) The powers are throwing it off...

Homework Statement Find the sum of the series e{(n + 1)/n)} - e^{(n + 2)/(n + 1)} The Attempt at a Solution Well for starters I got it into the proper format...IE (((n + 1)/(n))^n)/n! - (((n + 2)/(n + 1))^n)/n! But then I get a little lost...I would know how to take the limit...