(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

So the Airy equation states that y''-xy'=0. My problem is to proof that the improper integral

1/[tex]\pi[/tex] [tex]\int[/tex]cos(1/3*t^3+x*t) from 0 to [tex]\infty[/tex] satisfies this equation.

I've tried differentiating under the integral sign, but all I've gotten is the integrand to be

y''+ty = -1/pi [tex]\int[/tex] cos(1/3*t^3+x*t)(t^2+x) from zero to infinity. Naturally I do u substitution, but my final answer comes out to be -sin(infinity)/Pi

What should I be doing?

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Airy equation and solution

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