Recent content by Tom1

Homework Statement y''-2y'+2y = 0 Homework Equations y(0)=0 y'(0)=1 The Attempt at a Solution e^at sin(bt) I did this problem earlier with some help, but if someone could post the steps along the way so I could do a few more similar to it, I would appreciate it.

How are they related?

Can anyone help me get started please? I don't understand this at all and it's due soon.

Sorry, part of this seems to have been cut off. Assuming there is a slight background density of material with spherically symmetric density p1 falling off as p1 (alpha) r^-B Find the value of B in terms of alpha

Homework Statement A planet around a star has an orbit that is not exactly an ellipse. In addition to the dominant Fo \alpha r^-2 term due to gravity from the central star, the planet seems to be responding to a slight additional force which has the form F1 \alpha r^-\alpha where \alpha...

Thank you much for all your help.

Alright, I see now...but it causes another question to arise: When I go back to find the constants, I apply the initial conditions to solve for C&D, correct?

Just figured out how to use the tex feature to make it easier on your eyes. I'm a little confused about the variables: y(t) = Ae^{-t}C\cos t - Be^{-t}D\sin t Is that the solution?

Ah, I think I see my mistake. If u=1 then: y=(Ae^-t)cos(t)+(Be^-t)sin(-t)

Indeed, that's a mistake I commonly make. So with those solutions, the general solution of the IVP would be: y=c1(e^-t)cos(1)+c2(e^-t)sin(-1) ?

Assuming a=1, b=2 c=2 and r1= \lambda+i\mu r2=\lambda-i\mu r1=(-1+(-4)^1/2)/2 = -(1/2)+i(2)^(1/2) r2 = -(1/2)-i(2)^(1/2) Correct?

I have never done one with complex numbers before. Mind walking me through this one?

Homework Statement Solve the initial value problem: y''+2y'+2y=0 y(\pi/4)=2 y'(\pi/4)=-2 Homework Equations Included in 1 The Attempt at a Solution I assumed that y=e^rt and came up with the characteristic polynomial r^2+2r+2=0 but when solving it for the two roots, they come...

Hi, I am trying to decide whether y(t) = c1t^2 + c2 t^−1, where c1 and c2 are arbitrary constants, is the general solution of the differential equation (t^2)y'' − 2y = 0 for t > 0 and justify the answer, but I don't really know how to approach it from this "side" of the problem. Any suggestions...

The driving force just seems to be a function of angular frequency.