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.

 

[M98Ranger]

Your solution looks correct to me! It does not matter that the fourth and first orders are missing in the original equation, as long as the remaining orders are properly reduced to a first-order equation. Good job!