Query 26 Differential Equations

Question:  Find the solutions to y ' = A y when

A = [ 5, 3; -4, -3 ]

and

y(1) = [2; 0].

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Question:  Find the solutions to y ' = A y when

A = [ 4,2,0; 0,1,3; 0,0, -2 ]

and

y(0) = [-1;0;3].

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Question:  Three tanks, each full of a solution and all of equal volume V, are each connected to each of the others by two pipes.  Each tank also has a third pipe through which pure water flows into it, and a fourth through which water exits.

The flow rate r through every pipe is the same.

Write the system of equations that relates the quantities Q_1, Q_2 and Q_3 representing the amount of solute in each tank as a function of time.

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