Recent content by sassie

yes, y(0)=0 and y(1)=0

sorry, that was my fault. i wrote down the wrong ode, but mark44 pointed out the mistake. look's like I'm back at square 1.

Okay, thanks. I'll try that out :)

Oh, okay! I was pondering why your RHS was the way it was. But can you help me with getting the equation into a form where I can the general solution? I REALLY need a hint to get me on the right track. I am sure I can solve for the eigenvalues and eigenfunctions myself, it's just been getting...

Re: EDIT Yes, so I am trying to get the general solutions to the given equation but I do not know how to.

I haven't even got the general ODE and that's what I have been having problems with. I have absolutely no idea how to obtain it :'( I know it should be easy but for the life of me, I can't do it

But can anyone help me with this question? I've been working on it for 5 hours straight and still I can't a solution! This question is just so much harder than ones I have handled previously!

Okay, what I did was (sorry I did skip a few steps): LHS = -(1+x^2)y''-2xy'-(\lambda \frac{1}{1 + x^2}) y=0 I then multiplied through by (1+x^2) ((1+x^{2})^{2})y''+2x(1+x^{2}) + \lambda y =0 Now, I understand how you got the left hand side of the equation you gave, I am a little...

Homework Statement Evaluate and find the eigenvalues and eigenfunctions for: -\frac{d}{dx}[(1+x^{2})\frac{dy}{dx}]=\lambda\frac{1}{1+x^{2}}y} Homework Equations The Attempt at a Solution Okay, what I did was to expand the given equation to get: ((1+x^{2})^{2})y''+2x(1+x^{2})y' + \lambda y...

Please ignore. I figured out what I did wrong.

Consider the BVP y''+4y=f(x) (0\leqx\leq1) y(0)=0 y'(1)=0 Find the Green's function (two-sided) for this problem. Working: So firstly, I let y(x)=Asin2x+Bcos2x Then using the boundary conditions, Asin(2.0)+Bcos(2.0)=0 => B=0 y'(x)=2Acos(2x)-2Asin(2x) y'(0)=2A=0...

Homework Statement p(D) is a polynomial D operator of degree n>m. Suppose a is a m fold root of p(t)=0, but not a (m+1) fold root. Verify that \frac{1}{p(D)}e^{at}=\frac{1}{p^{(m)}(a)}t^me^{at} where p^{(m)}(t) is the m^{th} derivative of p(t).Homework Equations For this question, we were...

Homework Statement Find the solution for L[y]=H(t-pi/2)sint=q(t) y(0)=0 by using the Green's function. Homework Equations The Attempt at a Solution My problem is that I'm stuck with how to get the Heaviside into the required general solution. Is it anything to do with the fact that the...

So what would we get when we integrate \delta(t-\tau)? would it be 1?

Homework Statement Give the general solution to the IVP L[y]=y'+(sint)y=\delta(t-\tau) y(0)=0 For all t>0 by placing a jump condition on y(t) and solving the differential equation for t<\tau and t>\tau Homework Equations The Attempt at a Solution I'm plenty sure I can get the...