Question: how to do simple parametrization

sys := diff(y,t$3) + 3*diff(y,t$2) + 5*diff(y,t)  = diff(u,t$3) + diff(u,t$2) + diff(u,t)

x1 = diff(y,t)
x2 = diff(y,t$2)
x3 = diff(y,t$3)

how to do simple parametrization with x1, x2, x3 on sys, so that get 3 equations in terms of x1, x2, x3, u
result may be first order of x1, x2, x3

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