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Question: how to integrate by parts after multiply lambda(t) in this case

Question:how to integrate by parts after multiply lambda(t) in this case

ComputerUser 535 Maple
October 15 2013
0

Diff(x1(t),t) - x2(t) = 0;

Diff(x2(t),t) - x3(t) = 0;

Diff(x3(t),t) +3*x3(t) + 4*x2(t) + x1(t) = 2*Diff(u(t),t$2) + 5*Diff(u(t),t) + 7*u(t);

 

multiply above system by test functions -lambda1(t),-lambda2(t),-lambda3(t) and integrate by part

in order to find adjoint operator in the form

 

x1 -> Diff(lambda1(t),t) - lambda3(t) = miu1(t)

x2 -> Diff(lambda2(t),t) + lambda1(t) - 4*lambda3(t) = miu2(t)

x3 -> Diff(lambda3(t),t) + lambda2(t) - 3*lambda3(t) = miu3(t)

u  -> 2*Diff(lambda3(t),t$2) - 5*Diff(lambda3(t),t) + 7*lambda3(t) = miu(t)
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