# 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.

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#### ehild

Homework Helper
EvLer said:
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. :yuck:

Thanks

#### ehild

Homework Helper
EvLer said:
shoot...i need sleep. :yuck:

Thanks
Good night, sleep tight! :zzz:

ehild

#### GCT

Homework Helper
sleep...highly recommended

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