Reducing to First-Order Equation

[Banana]

Can someone double check me please? I'm not sure if it matters that the fourth and first orders are missing.

Reduce to a first-order equation:

2y''''' + 12x^3y''' - 2y^7y'' - 8y = 0

My solution:
u1' = u2
u2' = u3
u3' = u4
u4' = u5
u5' = -6x^3(u4) + y^7(u3) + 4(u1)

[Clausius2]

I think it's correct. First and fourth order do not appear because in original equation don't appear too.