B Solve ODE with Fractional Term: Find Solutions

[knockout_artist]

Hi,

This is equation I need to find solutions for
d²u/d²x + 1/2Lu = 0 where L(x)

I understand we can remove fraction from second term.
2 [d² u/d²x ] + Lu = 0

now how do I find solution of this equation ?

How do we deal with L ? because usually we have Y'(dy/dx or in this case du/dx ) or Y (in this case u) in second term in an ode.

Thanks.

 

[jim mcnamara]

d2u/d2x + 1/2Lu = 0 where L(x)

something seems missing here?

 

[knockout_artist]

ok we have to make characteristic equation out of it so I think

from this
2d²u/d²x + 1/2Lu = 0

following equation comes
2λ² + Lλ = 0