Recent content by BobMarly

Thank you for the comment. But the problem is what it is. Besides, I'm beginning to like Laplace. Seems like there are all kinds of possibilities. Multiply RHS by 2? Not sure I need to? The homogeneous part seems to be correct, which is the first term. I think the second term has to do with...

Homework Statement Use Laplace Transform to Solve IVP y"-2y'+2y=e^(-t) y(0)=0 y'(0)=1 Homework Equations [s^2*L{y}-sy(0)-y'(0)]-[2sL{y}-y(0)]+2L{y}=0 (for Homogeneous eq)The Attempt at a Solution Homogeneous Attempt: L{y}=1/(s^2-2s+2) Not sure if correct There soluton to this point is...

How do I know it satisfies the equation?

Not sure of solution for IVP Homework Statement (x^2)*y"+4*x*y'+4*y=0 y(1)=1 y'(1)=2 Homework Equations Start with r(r-1)+4r+4=0 then (r^2)+3r+4=0 get (-3+/-7i)/2 The Attempt at a Solution Leads to y=C(1)e^(-3t/2)cos(7t/2)+C(2)e^(-3t/2)sin(7t/2) More y'=... one large...

Prb:(x^4+4*x^2+16)y"+4(x-1)y'+6xy=0 P=(x^4+4*x^2+16) Q=4(x-1) R=6x P=0 for - 1 - 3^(1/2)*i 1 - 3^(1/2)*i - 1 + 3^(1/2)*i 1 + 3^(1/2)*i Q=0 for 1 R=0 for 0 Do we ignore Q & R, plotting P, then find shortest distance which would equal 2?

That was just a qoute I heard during an interview ten or twenty years ago. If you're looking for more info, dare I say Google It!

Yes, I'll read the notes. Thank you.

I've heard it stated that the most expensive part of a launch is the first 2 inches!

Maybe this is an easier question. What is the difference between x^n and a(n)x^n. The same, but only different? Is a(n)x^n used for power series? I'm sure these are one of the many processes to solving ODE. Maybe you can also point me in another direction. I understand the concept of ODE's and...

Yes, I understand. I thought there might be some quick answers. The book we are using doesn't seem to be the greatest for beginners. I've seen what looks to me better books from the library that are ten years old. I appreciate your help. Maybe you can suggest some books or resources. Any help...

Are these fundamental solutons? Or do I need initial values for a fundamental solution? Does this mean there are infinite amount of solutions, if so, is there a core of solutions? Or a center or solutions that the rest radiate out from?

I don't understand why we seem to be ignoring the (x^2) and x from the original formula? And why they are not involved in the general soluton?

Is this correct? (for the nonhomogeneous) n(n-1)x^n+nx^n-x^n=0 (n^2-n+n-1)x^n=0 (n-1)(n+1)=0 n=+/- 1 y=Ax+Bx=>y=x(A+B)

by substition I get: (x^2)(sum(n=2))a(n)x^(n-2)+x(sum(n=1))a(n)x^(n-1)-(sum(n=0))a(n)x^(n) Not sure what to do for n=0 for terms with (x^2) and x so I can end up with the (recurance relation)*x^n.

I end up with 4*x^2*(sum(n=0))(n+2)*(n+1)*a(n-2)*(x^n)+(sum(n=0))a(n)*(x^n) I'm working toward the recurance relation, correct? What about the 4*x^2 for the first summation?