- #1
dankaroll
- 13
- 0
Homework Statement
Use Fourier transform to find the solution of the following differential equation:
[tex]\frac{\mathrm{d^3}y }{\mathrm{d} x^3}+ \lambda \frac{\mathrm{dy} }{\mathrm{d} x} - xy = 0, \lim_{x \to \infty } y(x)=0[/tex]
Find the asymptotic of the solution for lambda>> 1. Normalize the solution so y(0) =1.
Homework Equations
Using differentiation properties of Fourier transform,
[tex]\frac{\mathrm{d^n}y }{\mathrm{d} x^n} = {(ik)^n }Y[f][/tex]
The Attempt at a Solution
using the property
[tex](ik)^3Y[f]+\lambda (ik)Y[f]-xY[f] =0 [/tex]
[tex]Y[f]((ik)^3+\lambda ik-x) = 0 [/tex]
so I'm slightly stuck here, since its zero on the right hand side...