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I'm having problem in finding $y''''$ if $y'=F(x,y)=f$ and $y''=fx + ffy$. Any help on this? I know that i will a multi variate chain rule since it is a function of two variables but i got confused later. what's the solution?

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2 Answers 2

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Example calculations are given on page 46 of Goursat, it really just amounts to applying the chain rule to $f(x,y)$.

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The calculations get rather intense. I have mathematica code here:

http://www.math.missouri.edu/~stephen/num-methods/5.4.runge.kutta.nb

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