Second order homog. DE non-const coeff.

[EvLer]

I have a 2nd order homogeneous non-const. coefficients linear DE, and don't remember how we used to solve it or even if we did at all, looked through the book, but it only covers a case of Cauchy-Euler.

The original question actually goes like this:
verify that y(x) = sin (x²) is in the kernel of L,
L = D² - x^-1D + 4x², where D is a differetiation operator.

so what I have so far is this:
Ly = 0
when I distribute I get this DE and get stuck with it:

y'' - x^-1y' + 4x²y = 0

Thanks for any help.

 

[ehild]

The original question actually goes like this:
verify that y(x) = sin (x²) is in the kernel of L,
L = D² - x^-1D + 4x², where D is a differetiation operator.

so what I have so far is this:
Ly = 0
when I distribute I get this DE and get stuck with it:

y'' - x^-1y' + 4x²y = 0

Thanks for any help.

This is a very simple question, just insert sin(x^2) for y.

ehild

 

[EvLer]

shoot...i need sleep.

Thanks

 

[ehild]

shoot...i need sleep.

Thanks

Good night, sleep tight! :zzz:

ehild

 

[GCT]

sleep...highly recommended