Recent content by faradayscat

It has length 'L' and density ρoil I'm not asking for a specific solution, just wanted to see if my work checks out.

The air pressure

Homework Statement [/B] Suppose we have a u-shaped tube filled with water, with oil added at one end which disturbs the equilibrium. Now say one end is blocked off and the other is exposed to air flow which reduces the pressure above the water and causes the water to climb back to equilibrium...

Thanks everyone, I have no further questions.

Yes, I forgot the vector 'x' next to the coefficient matrix. Thanks for your tips, I actually did the variation of parameters method and everything worked out after I checked my solution as Mark44 suggested.

I just checked, and its satisfied. Thanks!

Yes that's that I meant, sorry for the confusion. So could i set up a fundamental matrix with the homogeneous solutions and solve the non-homogeneous system with, say, variation of parameters? I tried and this is what I get: x(t) = c1e5t\left( \begin{array}\\ -1 \\ 2 \end{array} \right) +...

Yes, that's right. I'm not really familiar with Latex, I'll have to read up on it. I've edited my post, thanks

Homework Statement I want to solve this systemx' = \left( \begin{array}\\ 7 & 1 \\ -4 & 3 \end{array} \right)x + \left( \begin{array}\\ t \\ 2t \end{array} \right) Homework EquationsThe Attempt at a Solution i found the eigenvalues to both be 5. The eigenvector is (1,-2) and the generalized...

Quick question, can you solve non-homogeneous systems with repeated eigenvalues the same ways? i.e. variation of parameters, undetermined coefficients, etc... would the fundamental matrix contain the solution with the generalized eigenvalue? Thanks!

Ok, that actually makes sense now, thank you. I apologize for sounding frustrated, but the other person's answer wasn't very helpful as he simply replied "it's wrong, it should look like this (...)" without any further input. I didn't understand his answer so I asked for him to elaborate...

The latter is my solution... the point is to find the coefficients in terms of a0 and a1, right? That's exactly what I did, isn't it? When you solve homogeneous 2nd order differential equations, you assume a solution looks like y(x) = ert Right? Then you plug it into the DE and solve for...

Yeah, and I did not understand your answer. I'm asking for help and you just came on here to tell me I was wrong. Fine, I get it. I want to know what you mean by "it should look like this", if you don't want to help me then why did you even bother commenting on my thread?

Could you please elaborate on why you say it's wrong?

Yes, y(x) is the general solution of the differential equation represented as a power series. After finding the constants a2,a3,a4, etc I replaced them in y(x) and factored out the undetermined coefficients a0 and a1. Can you elaborate on what I did wrong?