# Separating a higher-order ODE into 1st-order ODEs

1. Sep 17, 2006

### Hawknc

Normally I can do these, and I'm fairly familiar with the equations used here, but for the life of me I can't figure this one out. Here's the question:

The following equation is the known as Blasius boundary layer equation for the laminar flow over a flat
plate in similarity variables:

2f''' + ff'' = 0
$\eta$ = 0, f' = f = 0
$\eta$ --> inf, f' --> 1

where

$$\eta = \frac{y}{x} \sqrt{\frac{U_{\infty}x}{\nu}$$

$$\frac{u}{U_\infty} = f'(\eta)$$

This'll look familiar to anyone else who knows fluid mechanics, I'm sure. The question requires me to solve this numerically using MATLAB, which I think I can figure out, but the methods we use require a series of 1st order ODES. I can't figure out how to separate this and it's driving me craaaaazy. Every method I try doesn't fit with the given boundary values. I've tried rearranging everything given there but I can't figure it out. Anyone got any ideas?

Last edited: Sep 17, 2006