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Question: Adjoint in DEtools seems different from book's example

Question:Adjoint in DEtools seems different from book's example

Ex 95 Maple
ode
May 27 2012
0

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
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