Is there a general formula that can be used to convert a 2nd order O.D.E into a system of two 1st order O.D.E's (or an Nth order O.D.E into a system of N 1st order O.D.E's)? F'rinstance, I'd like to convert the O.D.E.
y" - (1 - y2)y' + y = 0, [y(0) = .5, y'(0) = .5]
into two 1st order O.D.E's
u' = f(u, y)
y' = f(y, t)
...but I've no idea where to begin. I can solve 1st order O.D.E's without too much difficulty, but 2nd order O.D.E's are hating on me...
y" - (1 - y2)y' + y = 0, [y(0) = .5, y'(0) = .5]
into two 1st order O.D.E's
u' = f(u, y)
y' = f(y, t)
...but I've no idea where to begin. I can solve 1st order O.D.E's without too much difficulty, but 2nd order O.D.E's are hating on me...
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