@tomleslie The 4th condition :

diff( f(x,y), y$2) versus 'x' for y=Xval and 'x'= (say) 0..20 would be the question. Is it possible to plot a graph with this requirement? It seems to show error when I do so. Thank you for your time.

@tomleslie Thank you so much for your help, I tried it and it worked!

@Preben Alsholm Thank you so much for your help!

@Carl Love Thank you so much for your help! :) btw what does rhs(r[-1]) represent? and the [1],[y0}?

@tomleslie Thank you so much. yes, the modifications worked. Thanks alot.