any software help to see the Maple code inside the library with extension .lib?

> with(CurveFitting); data := [[2, 10], [3, 1], [5, 4], [7, 5]];
               [[2, 10], [3, 1], [5, 4], [7, 5]]
> PolynomialInterpolation(data, y);
                    3  3       2   199     143
      ...

i am looking for a command adjoint a ODE, to check whether my understanding of adjoint correct or not, when i find one example different from my understanding as follows

u*diff(Y,t) - diff(U,t) + diff(y,t)*U = 0 where uppercase and lowercase are different

why after adjoint is

Y -> -u*diff(lambda,t) - diff(u,t)*lambda = miu1
U -> diff(lambda,t) + diff(y,t)*lambda = miu2

why not

Y -> u*diff(lambda,t) = miu1
U -> -diff(lambda,t) + diff(y,t)*lambda = miu2

A := diff(Y,y$2)-(y11)^2*diff(Y,y) = 0
B := diff(diff(Y,x),y) - y11*diff(Y,x$2) = 0

do maple have tool to get differential identity, or simple algebra identity?
that identity is an equation in terms of A and B and y11, not Y

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