Sturm Liouville Form: Solving y''+(2/x)y'+[landa]y=0 Equation

[wolfandraven]

Homework Statement

y''+(2/x)y'+[landa]y=0, 0<x<1. y(0) must be finite, and y(1) = 0

Put this equation into sturm liouville form and state the weight function w(x)

Homework Equations

Sturm Liouville Form: {-d/dx(p(x)d/dx)+q(x)}y(x)=[landa]w(x)y(x)

The Attempt at a Solution

I'm almost certain the solution is {-d/dx(x^2dy/dx)=[landa]x^2y(x) so that w(x)=x^2

I just wanted to check that was correct because it comes right at the start of a computer project so it would be very annoying to find out I'd got that part wrong!

Thanks!

Gillian

 

[HallsofIvy]

Homework Statement

y''+(2/x)y'+[landa]y=0, 0<x<1. y(0) must be finite, and y(1) = 0

Put this equation into sturm liouville form and state the weight function w(x)

Homework Equations

Sturm Liouville Form: {-d/dx(p(x)d/dx)+q(x)}y(x)=[landa]w(x)y(x

The Attempt at a Solution

I'm almost certain the solution is {-d/dx(x^2dy/dx)=[landa]x^2y(x) so that w(x)=x^2

I just wanted to check that was correct because it comes right at the start of a computer project so it would be very annoying to find out I'd got that part wrong!

Thanks!

Gillian

Yes, that is correct.

 

[wolfandraven]

Great, thanks!