How to transform into first order system?

Hi, I have questions on hot to transform these ODE into first order system. I already have the assumption but I just dont understand how?

This is the perturbation equations need to be transformed:

[i*alpha+(1/R)]*u+i*beta*v+Du+Dw=0
[-i*omega+U*i*alpha+V*i*beta+(U/R)]*u-[2*(V+1)/R]*v+DU*w+alpha*p*i+(W/R)*Du-(1/R)*(mu*D^2u+Dmu*Du)=0
[-i*omega+U*i*alpha+V*i*beta+(U/R)]*v-[2*(V+1)/R]*u+DV*w+beta*p*i+(W/R)*Dv-(1/R)*(mu*D^2v+Dmu*Dv)=0
[-i*omega+U*i*alpha+V*i*beta+(DW/R)]*w-[W/R]*Dw+Dp+(1/R)*D(mu*Dw)=0

And the perturbation equations then transformed into a set of six first order ode by using these transformed variables:

eta1=[alpha-(i/R)]*u+beta*v
eta2=[alpha-(i/R)]*Du+beta*Dv
eta3=w
eta4=p
eta5=[alpha-(i/R)]*v-beta*u
eta6=[alpha-(i/R)]*Dv-beta*Du

So my question is, how to choose the transformed variables? How did the get these transformed variables? Thank you.