# Bounday-Value Problem: Eigenvalue and Eigenfunctions

1. Jul 15, 2008

### physicsfan24

1. The problem statement, all variables and given/known data
This is the original question:
$$\frac{d^{2}y}{dx^{2}}-\frac{6x}{3x^{2}+1}\frac{dy}{dx}+\lambda(3x^{2}+1)^{2}y=0$$

(Hint: Let t=$$x^{3}+x$$)
y(0)=0
y($$\pi$$)=0

2. The attempt at a solution
This might be all wrong, but this is all I can think of
$$\frac{dt}{dx}=3x^{2}+1$$

so $$\frac{d^{2}y}{dx^{2}}-\frac{6x}{\frac{dt}{dx}}\frac{dy}{dx}+\lambda(\frac{dt}{dx})^{2}y=0$$

After this, I do not know how to proceed to eliminate $$d^{2}y/dx^{2}$$, much less what else to do. Help!

Thank you very much for your time,
-PhysicsFan24

Last edited: Jul 15, 2008
2. Jul 15, 2008

### camilus

holy **** bro are you in my class, MIAMI DADE DEs?? LOL and were both on here lookin 4 help here.

check out my thread, its the whole paper lol. yo you got the answers for any of the others??

3. Jul 15, 2008

### physicsfan24

Umm, I'm in U of Virgina and this is an online HW question... Yes I am taking ODE. You're in my class?

4. Jul 15, 2008

### camilus

nevermind. Im in Miami Florida. But I got the same question as you at the same time. One hell of a coincidence. Let me know if you find the answer, and you can check my thread too, I got the same question posted on there.