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setting F=de2.rhs(), can you use that dF/dy = dF/dt / (dy/dt) ? Would the following do the trick?
sage: F=de2.rhs()
sage: (diff(F,t) / diff(y(t),t)).subs(de1).subs(de2)
-(3*(y(t)^3 + a*x(t) + (a - 4)*y(t)/a)*y(t)^2 - a*y(t) + (y(t)^3 + a*x(t) + (a - 4)*y(t)/a)*(a - 4)/a)/(y(t)^3 + a*x(t) + (a - 4)*y(t)/a)
For the other derivatives a similar approach should apply.
