Solving Airy's Equation: Numerical Method & Steps

[robbin53]

Numerically solve for the solution of Airy's equation y''=xy on the interval 0<x<1 with boundary conditions y(0)=y'(0)=1. Use the trial solution

yhat = 1 + x + (sumation j = 2 through N) csubj*x^j.

Where do I get started? I am so lost.

 

[CPL.Luke]

hmm I can't really understand the sumattion you posted, but normally you would assume that the solution takes the form of an infinite power series.

then you plug in for y and y' and simplify.

 

[robbin53]

Thanks, I started that to do that, I'm glad I'm going about it the right way!