Reducing third order ODE to a system of first order equs + 4th order runge-kutta

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TTM
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Hi,
I am stuck on the initial steps of this problem - its been a while since my diff. eq course.
I need to reduce this into a system of three equations then apply a 4th order runge kutta method to solve.

Homework Statement


f'''+f*f''=0
Boundary conditions:
f'(0)=f(0)=0
f'(infinity)=0

A. Reduce this equation to a system of three first order equations, with associated boundary conditions.

The Attempt at a Solution


Am I on the right track?
(equation 1) f'=g
(2) g'=h
(3) h'=-f*h

how to apply boundary conditions?
 

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