>>11619387I would try to find individual first order integrals of :
Ax' - Bxy^(1.75) dx''
Cy' -Dyz-Ey^(1.75x) dy''
Fz' -Gyz-Hxy^(1.75) dz''
alternatively, you could analyze it intuitively by thinking of a discrete infinite series:
t = 1, 2, 3 ... inf
x'(t) =t = 1, 2, ,3 ... inf
Ax't = A*0, A*1....
now you have 3 series:
t = 1, 2, 3...
x't = 1, 2, 3...
Ax't = 0, A, 2A ...
you can now keep doing this for all polynomials in your system - derive their discrete series from your assumed discrete seed t.
x''t = (x'(t)) ' = 0, 0, 0....
after you finish the first equation, you can start describing the others with what you have. such that x in the second equation is the discrete series 1,2,3... etc.
try actually plugging in the constants into the series which have them, and derive the relationship as if its a nested loop, where the first loop is a for loop along t ( t1 = 1,t2 = t1+1,t3 = t2 +1 ...) and the rest are nested for loops which include t in them ( x1 = t1, x2 =t2)
the reason this is legal is that you are dealing with strictly variables and constants, so any variable can be any variable as long as you keep the system consistant. if you know how to program you could just try and write it a program which iteratively calculates the derivative of any contiguous function by assuming that it is actually discrete.
