I need to reduce the following system to a single higher-order linear ODE for y

x'(t) - y'(t) + z(t) = 0

x(t) + y'(t) - z'(t) = 1

y(t) + z'(t) = t^{3}- 1

I've tried setting ( z = y' - x' ) & (x = 1 - y' - z')

However on substituting these it ends up as a big mess and I can't go anywhere. Could you someone tell me what substitution or technique I should use to work this problem?

Thanks.